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anonymous
 one year ago
Will METAL!!
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x) = the quantity x minus seven divided by the quantity x plus three. and g(x) = quantity negative three x minus seven divided by quantity x minus one.
anonymous
 one year ago
Will METAL!! Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = the quantity x minus seven divided by the quantity x plus three. and g(x) = quantity negative three x minus seven divided by quantity x minus one.

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phi
 one year ago
Best ResponseYou've already chosen the best response.1ooh. Time to use the equation editor.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443790834332:dw

phi
 one year ago
Best ResponseYou've already chosen the best response.1the first part f( g(x) ) means everywhere you see x in f(x), replace it with g(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how exactly do I replace it.

phi
 one year ago
Best ResponseYou've already chosen the best response.1the first step is \[ f( g(x) ) = \frac{g(x) 7}{g(x)+3} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1but g(x) is also the messy \( \frac{3x7}{x1} \) so we put that expression in for g(x)

phi
 one year ago
Best ResponseYou've already chosen the best response.1btw, for future reference metal (iron or copper) is different from medal (shiny doodad)

phi
 one year ago
Best ResponseYou've already chosen the best response.1everywhere you see g(x) in \[ \frac{g(x) 7}{g(x)+3} \] erase the g(x) and replace it with \[ \frac{3x7}{x1} \] you get a big mess, but it will simplify with some algebra

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(3x7)7  (x1)+3

phi
 one year ago
Best ResponseYou've already chosen the best response.1\[ \frac{\frac{3x7}{x1}7}{\frac{3x7}{x1}+3} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1that is how you replace g(x) with the messy fraction

phi
 one year ago
Best ResponseYou've already chosen the best response.1to simplify , I would multiply top and bottom by (x1) \[ \frac{\left(\frac{3x7}{x1}7\right)}{\left(\frac{3x7}{x1}+3\right)} \cdot \frac{(x1)}{(x1)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so would that cancel out x1 or...

phi
 one year ago
Best ResponseYou've already chosen the best response.1do the top first: distribute the (x1) (which means multiply both terms inside by (x1)

phi
 one year ago
Best ResponseYou've already chosen the best response.1the top is \[ \left(\frac{3x7}{x1}7\right)(x1) \\ \frac{3x7}{(x1)}(x1) 7(x1) \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1can you simplify the top ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes, 3x  (x1) x1 I'm not sure

phi
 one year ago
Best ResponseYou've already chosen the best response.1\[ \frac{3x7}{(x1)}(x1) \] that is the first term, the (x1) cancels

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if the bottom cancels then the top is 3x7

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes. and the 2nd term is 7(x1) if you distribute the 7 what do you get ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1there is no = sign, just 3x7+ 7x + 7 (that mess simplified to that) now combine like terms

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes the top (of the original fraction) simplifies to 10x now we do the bottom \[ \left(\frac{3x7}{x1}+3\right)(x1) \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you said the bottom right?

phi
 one year ago
Best ResponseYou've already chosen the best response.1the (x1) times the first term will cancel the (x1) in the botom

phi
 one year ago
Best ResponseYou've already chosen the best response.1in case you lost track, we are doing the bottom of this mess: \[ \frac{\left(\frac{3x7}{x1}7\right)}{\left(\frac{3x7}{x1}+3\right)} \cdot \frac{(x1)}{(x1)} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1we found that \[ \frac{\left(\frac{3x7}{x1}7\right)}{\left(\frac{3x7}{x1}+3\right)} \cdot \frac{(x1)}{(x1)} = \frac{10x}{\left(\frac{3x7}{x1}+3\right)(x1)} \] and we are doing the bottom \[ \left(\frac{3x7}{x1}+3\right)(x1)\]

phi
 one year ago
Best ResponseYou've already chosen the best response.1and the bottom \[ \left(\frac{3x7}{x1}+3\right)(x1)\\ \frac{3x7}{(x1)}(x1)+3(x1) \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0x1 cancels out so 37 is 4 so 34.

phi
 one year ago
Best ResponseYou've already chosen the best response.1x1 cancels so you are left with 3x7 (for the first term)

phi
 one year ago
Best ResponseYou've already chosen the best response.1\[ \frac{3x7}{\cancel{(x1)}}\cancel{(x1)}+3(x1) \\ 3x7 +3(x1) \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1now distribute the 3 in the 2nd term

phi
 one year ago
Best ResponseYou've already chosen the best response.1ok, so the bottom simplifies to 10 we found that \[ f(x) = \frac{\frac{3x7}{x1}7}{\frac{3x7}{x1}+3} = \frac{10x}{10} \] one more step to go

phi
 one year ago
Best ResponseYou've already chosen the best response.1you can't ignore the x remember if you have \[ \frac{10 \cdot x }{10} \] that is the same as \[ \frac{10}{10} \cdot \frac{x}{1} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes or just x you just showed f( g(x) ) = x the question was ***Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. *** you just did the first part. now they want to do it the "other way" show g( f(x) ) = x I hope you are a "highenergy" person, because it's more work.

phi
 one year ago
Best ResponseYou've already chosen the best response.1it's almost right, g(x) is (3x7)/(x1)

phi
 one year ago
Best ResponseYou've already chosen the best response.1it can get confusing unless we are slow and methodical \[ g(x) = \frac{3x7}{x1} \\ g( f(x)) = \frac{3f(x)7}{f(x) 1} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1now replace f(x) with its expression \[ g( f(x)) = \frac{3\frac{x7}{x+3}7}{\frac{x7}{x+3} 1} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1do you follow this part \[ g(x) = \frac{3x7}{x1} \\ g( f(x)) = \frac{3f(x)7}{f(x) 1} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1and f(x) is "shorthand" (or the name for) \[ \frac{x7}{x+3} \] so everywhere we see f(x), we can put in the "long form"

phi
 one year ago
Best ResponseYou've already chosen the best response.1\[ g( f(x)) = \frac{3f(x)7}{f(x) 1} \] the top says "multiply 3 times f(x)" then subtract 7 in math, and replacing f(x) with its expression, we would write 3 * (x7)/(x+3) then subtract 7: 3 * (x7)/(x+3) 7 \[ 3 \cdot \frac{x7}{x+3}  7\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh yea cancel out x3 right

phi
 one year ago
Best ResponseYou've already chosen the best response.1we haven't gotten that far, but that will be the idea. First, do you see how we get \[ g( f(x)) = \frac{3\frac{x7}{x+3}7}{\frac{x7}{x+3} 1} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1now you see the (x+3) that would be nice to get rid of. multiply top and bottom by (x+3)

phi
 one year ago
Best ResponseYou've already chosen the best response.1\[ \frac{\left(3\cdot \frac{x7}{x+3}7\right)(x+3)}{\left(\frac{x7}{x+3} 1\right)(x+3)} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1can you do the top ? post your steps. the first step is "distribute" the (x+3)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I thought x+3 cancels out?

phi
 one year ago
Best ResponseYou've already chosen the best response.1distribute means multiply each term inside the parens for example: (a + b)(x+3) = a(x+3) + b(x+3) use that same rule on \[ \left(3\cdot \frac{x7}{x+3}7\right)(x+3) \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.03(x7)7 3x+217 3x+14 ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1"terms" are things multiplied together. the 3 * (x7)/(x+3) is all one term terms are separated by + or . in other words, the 7 is also a term Here is what it looks like, after distributing the (x+3) \[ \left(3\cdot \frac{x7}{x+3}7\right)(x+3)\\ 3\cdot \frac{x7}{x+3}\cdot (x+3) 7 \cdot (x+3) \] notice the 7 is also multiplied by (x+3)

phi
 one year ago
Best ResponseYou've already chosen the best response.1you did the first part correctly. 3(x7) but you also have 7(x+3)

phi
 one year ago
Best ResponseYou've already chosen the best response.13(x7) + 7(x+3) try again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.03x7+7x+21 10x+14

phi
 one year ago
Best ResponseYou've already chosen the best response.1ok but how are you doing 3(x7) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ugh I messed up again. 3x+21+7x21

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, that looks good. now we do the bottom \[ \left(\frac{x7}{x+3} 1\right)(x+3) \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1can you distribute (x+3) by writing (x+3) next to each term inside the parens?

phi
 one year ago
Best ResponseYou've already chosen the best response.1ok, so we have \[ g( f(x) ) = \frac{10x}{10} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, so you have shown that f(g(x))= x and g(f(x))= x which proves that f(x) and g(x) are inverses.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you soo much :) can we do one more problem it won't take that long.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Find the angle θ (if it exists) in the interval [0°, 90°) for which sin θ = cos θ. θ = 30° θ = 45° No such angle exists. θ = 60°

phi
 one year ago
Best ResponseYou've already chosen the best response.1divide both sides by cos theta

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, you get sin x/cos x = 1 tan x = 1 x= atan 1 = 45º

phi
 one year ago
Best ResponseYou've already chosen the best response.1or you can remember that sin 45 = sqr(2)/2 and cos 45 = the same thing
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