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 2 years ago
Can somebody just check me? For the function f(x) = (3 – 4x)², find f–1. Determine whether f–1 is a function. Is this right? what i have:
f(x)=(34x)^2
f(1)=(34x1)^2
=(34)^2
=(1)^2
=1
f is a function
 2 years ago
Can somebody just check me? For the function f(x) = (3 – 4x)², find f–1. Determine whether f–1 is a function. Is this right? what i have: f(x)=(34x)^2 f(1)=(34x1)^2 =(34)^2 =(1)^2 =1 f is a function

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whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1Aren't you supposed to find the inverse?

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1im just so confuse.... i have no idea what im doing

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1Is it written like this? \[f(x) = (34x)^2, find f^{1}(x)\]

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1Okay, yeah, that's finding the inverse function and checking if that is a function, not evaluating the original function at f(1) or f(1)... So, do you know how to find the inverse function?

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1ohh1! nope i honestly do not remember

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1wait you switch the x and y right?

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1Okay, if you want to find the inverse function, you write out the original function as y = f(x) = (34x)^2, but then you swap x and y, and rearrange it as y = <some function> For example, if you had y = f(x) = 3x, f^(1)(x) would be found like this: y = 3x x = 3y x/3 = y so y = x/3 would be the inverse of y = 3x.

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1ok so in my example would it be.. y = (3 – 4x)² x = (34y)^2

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1so after the dust settles, what does y = ?

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1so x = (34y)^2 y= 1/4 (3sqrt(x)) so... f^1 = 1/4 (3sqrt(x))

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1Won't 1/4 (3 + sqrt(x)) = y also?

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1yes so it would be y = (1/4)( 3 ± sqrt(x))

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1Right. So, is the inverse a function?

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1f1(x) = y = (1/4)(3 ± sqrt(x)) ??

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1oh no sorry its not a function!

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1That's right, it fails the vertical line test. A vertical line passes through the curve more than once, so there is not a unique value of y for every x.

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1If you draw a line through the origin heading up and to the right at a 45 degree angle (slope = 1), the inverse function is simply the original function reflected along that line. So if you have a parabola opening upward centered on the yaxis, the inverse is a parabola opening to the right centered on the xaxis.

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1And a little thought about that suggests that functions more complicated than straight lines may not have an inverse which is a function...

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1oh okay! i see what your saying now! you explained it to me well! thank you for your help!! (:

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1Glad I could help make the little bulb come to life :)

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1little light bulb that is

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1hahah you are awesome! can you maybe help me with one more?

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1Use the Change of Base Formula to evaluate log7(76)

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1like would it be log7(76)= log(76)/log10(7) is that the answer?

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1\[\log_b a = \frac{\log a }{\log b}\] So \[\log_7 76 = \frac{\log{76}}{\log 7}\]

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1Both of the logs on the right hand side need to be in the same base, of course. Do you know how you can show that this is true?

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1wait so would it be log76 = 1.88081359 and log 7= 84509804 and you would divide those right?

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1Yes, but I think you are missing a decimal in your value of log 7...

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1oh yeah i did! so it would .84509804

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1so the answer would be 2.22556685

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1\[\log_b a = \frac{\log a}{\log b}\]Raise both sides as powers of b \[b^{\log_b a} = b^{\frac{\log a}{\log b}}\]But the left half of that is simply a by definition \[a = b^{\frac{\log a}{\log b}}\]and if we take the log of both sides \[\log a = \frac{\log a}{\log b}*\log b\]because \[\log u^n = n \log u\]

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1As a quick check of your answer, 7^2*(7*1/5) = 68.6, and 7^2*(7*1/4) = 85 so it looks like the answer is in the right ballpark. 7^2.225 is a little bit bigger than 1/5, and a little smaller than 1/4.

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1so my answer was right?

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1ah thank you again!!!!!

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1Now you can go tutor all of your friends :) That's a good way to reinforce your grasp of the material — try to explain it to someone else. Works best if they can ask questions in return, so explaining it to the cat or dog might not be as effective :)

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1I think I will! you are amazing thank you again, and I usually get confused but you made me understand!! :)

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1\[\sqrt{7}(\sqrt{x}7\sqrt{7}\]

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1Is that supposed to be \[\sqrt{7}(\sqrt{x}7\sqrt{7})\] and is the goal to simplify it?

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1oh yes sorry! Multiply and simplify if possible.

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1Well, if you distribute it out, what do you get?

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1\[\sqrt{7x}49\sqrt{x}\]

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1where did the \sqrt{x} next to the 49 come from?

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1i have no idea.. how do you distribute that?

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1Well, multiply sqrt(7) by the first term in the parentheses, and you get sqrt(7)sqrt(x). Multiply sqrt(7) by the second term in the parentheses, and you get sqrt(7)*7*sqrt(7), right?

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1and that last bit reduces to 49

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1\[\sqrt{7x}49 = \sqrt{7}\sqrt{x}49\] (I'd probably write the first one if it was a final answer, the second if I was going to do further canceling or manipulation).

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1\[a(bc) = ab  ac, a = \sqrt{7}, b=\sqrt{x}, c = 7\sqrt{7}\]

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1wait whats the answer.. im lost

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1See my post with the (I'd probably write ...) The last bit was just showing why the second term shouldn't have an x in it

whadduptori
 2 years ago
Best ResponseYou've already chosen the best response.1Oh I see what you were doing now! sorry

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.1Not a problem. If we were talking, I would have said a bit more, and you would have understood right away.
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