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monkey*
 one year ago
Given f(x)=x^2+7 and g(x)=x4/x. Find (g o f)(1).
Hint: (g o f)(1)=g(f(1))
monkey*
 one year ago
Given f(x)=x^2+7 and g(x)=x4/x. Find (g o f)(1). Hint: (g o f)(1)=g(f(1))

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freckles
 one year ago
Best ResponseYou've already chosen the best response.1so have you tried finding f(1) and then finding g(put result of f(1) here)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1f(1) tells us to use f(x)=x^2+7 we know to use f(x)=x^2+7 because of the f in f(1)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1f(x)=x^2+7 we can see here the input is the thing in f( ) example: f(a)=a^2+7 f(a+1)=(a+1)^2+7 f(input)=(input)^2+7 another example; f(2)=2^2+7 can you find f(1)=?

monkey*
 one year ago
Best ResponseYou've already chosen the best response.0I'm a little lost, sorry.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1ok do you see that f(x)=x^2+7 and you are also to find f(1)?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1f(x)=x^2+7 since we want to find f(1) we need to replace those x's with 1

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so can you find f(1)?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440459828779:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1let me know when you have found f(1)

monkey*
 one year ago
Best ResponseYou've already chosen the best response.0Would it be f(1)1^2+7?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well there should be an equal sign somewhere there

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1440460061483:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.1can you simplify (1)^2+7?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1yes f(1)=(1)^2+7=(1)(1)+7=1+7=8 so f(1)=8 so f(1) is 8 now we had to find g(f(1)) we just found that inside thing the f(1) thing to be 8 replace f(1) with 8 you are now really wanting to find g(8)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1g(8) tells us to use the expression named g

freckles
 one year ago
Best ResponseYou've already chosen the best response.1g looks likes g(x)=x4/x

freckles
 one year ago
Best ResponseYou've already chosen the best response.1just replace the old input x with the new input 8

freckles
 one year ago
Best ResponseYou've already chosen the best response.1simplify and then you are done

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you have to replace all the x's with 8 not just one of the x's

freckles
 one year ago
Best ResponseYou've already chosen the best response.1whatever you replace the first x with you have to replace the other x's on the other side also

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I don't think teachers like unsimplified answers :p

monkey*
 one year ago
Best ResponseYou've already chosen the best response.0And no, they don't lol.

monkey*
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much for the help!

freckles
 one year ago
Best ResponseYou've already chosen the best response.1for me to check your answer I have to know one this is it \[g(x)=\frac{x4}{x} \text{ or } g(x)=x\frac{4}{x}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so it is actually g(x)=(x4)/x not g(x)=x4/x so g(8)=(84)/8=4/8=1/2 or .5

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[f(x)=x^2+7 \\ g(x)=\frac{x4}{x} \\ g(f(1)) = g((1)^2+7)=g(1+7)=g(8)=\frac{84}{8}=\frac{4}{8}=\frac{1}{2}\]

monkey*
 one year ago
Best ResponseYou've already chosen the best response.0So what would be the answer?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well we just got that g(f(1))=1/2 and we were looking for the value of g(f(1)) so we are done

monkey*
 one year ago
Best ResponseYou've already chosen the best response.0So .5 would be the answer?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1yes a half is the answer

freckles
 one year ago
Best ResponseYou've already chosen the best response.11/2 or .5 you choose the form or write in the desired form your teacher wants

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I like pretty fractions so I would write 1/2 :p

monkey*
 one year ago
Best ResponseYou've already chosen the best response.0Okay, thanks. And she wants a fraction. Could you help with one more?

monkey*
 one year ago
Best ResponseYou've already chosen the best response.0Determine the standard form of the equation of the line that passes through (7,8) and (0,8).

monkey*
 one year ago
Best ResponseYou've already chosen the best response.0Determine the standard form of the equation of the line that passes through (7,8) and (0,8).

freckles
 one year ago
Best ResponseYou've already chosen the best response.1point slope form for a line looks like: \[yy_1=m(xx_1) \\ \text{ where } m \text{ is the slope of the line } \\ \text{ and } (x_1,y_1) \text{ is a point on the line }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you might want to go ahead and find m first

freckles
 one year ago
Best ResponseYou've already chosen the best response.1if you have two points you can find m by using the following formula: \[m=\frac{y_2y_1}{x_2x_1}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1we do have two points so we can use that formula

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[(x_1,y_1) \text{ and } (x_2,y_2) \\ (7,8) \text{ and } (0,8) \\ \text{ so replace } x_1 \text{ with } 7 \\ \text{ and replace } y_1 \text{ with } 8 \\ \text{ replace } x_2 \text{ with } 0 \\ \text{ finally replace } y_2 \text{ with } 8 \\ m=\frac{y_2y_1}{x_2x_1}=\frac{88}{0(7)}\] yes if you mean m=(88)/(0(7))

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and yes you simplify this value for m that we just found

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so 88=(8+8)=16 right and what about the bottom 0(7)=(7)=...

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[yy_1=m(xx_1) \\ \text{ where } m \text{ is the slope of the line } \\ \text{ and } (x_1,y_1) \text{ is a point on the line } \\ \] \[(x_1,y_1) \text{ and } (x_2,y_2) \\ (7,8) \text{ and } (0,8) \\ \text{ so replace } x_1 \text{ with } 7 \\ \text{ and replace } y_1 \text{ with } 8 \\ \text{ replace } x_2 \text{ with } 0 \\ \text{ finally replace } y_2 \text{ with } 8 \\ m=\frac{y_2y_1}{x_2x_1}=\frac{88}{0(7)}\] so let's go back to our point slope form for a line... \[yy_1=m(xx_1) \\ \text{ we just found } m \text{ to be } \frac{16}{7} \\ \\ \text{ replace } m \text{ with } \frac{16}{7}\] \[yy_1=\frac{16}{7}(xx_1)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1now really the last thing to do is put in x1 and y1

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you can use the value I called x1 and y1 above

freckles
 one year ago
Best ResponseYou've already chosen the best response.1that is all that is really left is to replace x1 and y1 have you done that?

monkey*
 one year ago
Best ResponseYou've already chosen the best response.0No, I'm confused about that.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1" \[yy_1=m(xx_1) \\ \text{ where } m \text{ is the slope of the line } \\ \text{ and } (x_1,y_1) \text{ is a point on the line } \\\] \[(x_1,y_1) \text{ and } (x_2,y_2) \\ (7,8) \text{ and } (0,8) \\ \text{ so replace } x_1 \text{ with } 7 \\ \text{ and replace } y_1 \text{ with } 8 \\ \text{ replace } x_2 \text{ with } 0 \\ \text{ finally replace } y_2 \text{ with } 8 \\ m=\frac{y_2y_1}{x_2x_1}=\frac{88}{0(7)}\] so let's go back to our point slope form for a line... \[yy_1=m(xx_1) \\ \text{ we just found } m \text{ to be } \frac{16}{7} \\ \\ \text{ replace } m \text{ with } \frac{16}{7}\] \[yy_1=\frac{16}{7}(xx_1)\] " You should see somehwere here that I called a number x1 and I called a number y1...

freckles
 one year ago
Best ResponseYou've already chosen the best response.1remember the point (7,8) ?

monkey*
 one year ago
Best ResponseYou've already chosen the best response.0Yes! I feel stupid now.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1remember the last thing really is just to replace x1 with 7 and y1 with 8..

freckles
 one year ago
Best ResponseYou've already chosen the best response.1thought this form we are looking at is pointslope form

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and your question asks for standard form

freckles
 one year ago
Best ResponseYou've already chosen the best response.1ax+by=c <so this is the form we want

freckles
 one year ago
Best ResponseYou've already chosen the best response.1your line should be \[y8=\frac{16}{7}(x(7)) \\ \text{ or you could have actually used the point } (x_2,y_2) \text{ instead } \\ y(8)=\frac{16}{7}(x0) \\ \text{ doesn't matter you just have to plug in a point that is on the line for } \\ (x_1,y_1)\] so either one we play with will give us the same answer... you pick the first one or second one... I honestly think the second one looks prettier

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[y+8=\frac{16}{7}x \\ \text{ note: all I did here was do } (8)=8 \text{ and } x0=x \\ \text{ anyways we have so far } y+8=\frac{16}{7}x \\ \text{ we want our } x \text{ terms and } y \text{ terms on the same side } \\ \text{ so subtract } y \text{ on both sides } 8=\frac{16}{7}xy \\ \] in some people's eyes this may be done by some prefer the number in front of x to be positive so you you can multiply both sides by 1 \[8=\frac{16}{7}x+y\] now some prefer just to also have integers coefficients and 16/7 is definitely not an integer so you could also multiply both sides by 7 \[56=16x+7y\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1this is probably the most secure way to write it because it fits everyones' expectation of standard form for a line

freckles
 one year ago
Best ResponseYou've already chosen the best response.1Ax+By=C A is positive integer B is integer C is integer I think this is the most strict definition of a line in standard form

monkey*
 one year ago
Best ResponseYou've already chosen the best response.0I have another one just like this except the points are (9,4) and (6,4). I do everything the same way, right?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1put in point slope form then put in standard form
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