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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
 one year ago
 one year 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
 one year ago
 one year ago

This Question is Closed

whpalmer4Best ResponseYou've already chosen the best response.1
Aren't you supposed to find the inverse?
 one year ago

whadduptoriBest ResponseYou've already chosen the best response.1
im just so confuse.... i have no idea what im doing
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
Is it written like this? \[f(x) = (34x)^2, find f^{1}(x)\]
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
Okay, 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?
 one year ago

whadduptoriBest ResponseYou've already chosen the best response.1
ohh1! nope i honestly do not remember
 one year ago

whadduptoriBest ResponseYou've already chosen the best response.1
wait you switch the x and y right?
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
Okay, 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.
 one year ago

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

whpalmer4Best ResponseYou've already chosen the best response.1
so after the dust settles, what does y = ?
 one year ago

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

whpalmer4Best ResponseYou've already chosen the best response.1
that's half of it...
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
Won't 1/4 (3 + sqrt(x)) = y also?
 one year ago

whadduptoriBest ResponseYou've already chosen the best response.1
yes so it would be y = (1/4)( 3 ± sqrt(x))
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
Right. So, is the inverse a function?
 one year ago

whadduptoriBest ResponseYou've already chosen the best response.1
f1(x) = y = (1/4)(3 ± sqrt(x)) ??
 one year ago

whadduptoriBest ResponseYou've already chosen the best response.1
oh no sorry its not a function!
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
That'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.
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
If 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.
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
And a little thought about that suggests that functions more complicated than straight lines may not have an inverse which is a function...
 one year ago

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

whpalmer4Best ResponseYou've already chosen the best response.1
Glad I could help make the little bulb come to life :)
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
little light bulb that is
 one year ago

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

whadduptoriBest ResponseYou've already chosen the best response.1
Use the Change of Base Formula to evaluate log7(76)
 one year ago

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

whpalmer4Best ResponseYou've already chosen the best response.1
\[\log_b a = \frac{\log a }{\log b}\] So \[\log_7 76 = \frac{\log{76}}{\log 7}\]
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
Both 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?
 one year ago

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

whpalmer4Best ResponseYou've already chosen the best response.1
Yes, but I think you are missing a decimal in your value of log 7...
 one year ago

whadduptoriBest ResponseYou've already chosen the best response.1
oh yeah i did! so it would .84509804
 one year ago

whadduptoriBest ResponseYou've already chosen the best response.1
so the answer would be 2.22556685
 one year ago

whpalmer4Best 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 \[\log u^n = n \log u\]
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
As 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.
 one year ago

whadduptoriBest ResponseYou've already chosen the best response.1
so my answer was right?
 one year ago

whadduptoriBest ResponseYou've already chosen the best response.1
ah thank you again!!!!!
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
Now 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 :)
 one year ago

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

whadduptoriBest ResponseYou've already chosen the best response.1
\[\sqrt{7}(\sqrt{x}7\sqrt{7}\]
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
Is that supposed to be \[\sqrt{7}(\sqrt{x}7\sqrt{7})\] and is the goal to simplify it?
 one year ago

whadduptoriBest ResponseYou've already chosen the best response.1
oh yes sorry! Multiply and simplify if possible.
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
Well, if you distribute it out, what do you get?
 one year ago

whadduptoriBest ResponseYou've already chosen the best response.1
\[\sqrt{7x}49\sqrt{x}\]
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
where did the \sqrt{x} next to the 49 come from?
 one year ago

whadduptoriBest ResponseYou've already chosen the best response.1
i have no idea.. how do you distribute that?
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
Well, 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?
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
and that last bit reduces to 49
 one year ago

whpalmer4Best 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).
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
\[a(bc) = ab  ac, a = \sqrt{7}, b=\sqrt{x}, c = 7\sqrt{7}\]
 one year ago

whadduptoriBest ResponseYou've already chosen the best response.1
wait whats the answer.. im lost
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
See 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
 one year ago

whadduptoriBest ResponseYou've already chosen the best response.1
Oh I see what you were doing now! sorry
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
Not a problem. If we were talking, I would have said a bit more, and you would have understood right away.
 one year ago
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