Question

Given the function f(x) = 0.3(4)x, what is the value of f^(−1)(6)?

Answer 1

I am assuming that f^(-1) means the inverse function, and you are plugging 6 in. So to get the inverse of a function, you can switch the x and y and then solve for y. So in your example you have y=.3(4)x. Switch x and y here, and solve for y, then plug in 6 into your inverse function.

Answer 2

where would 6 be plugged in

Answer 3

I just did this,
Step 1: replace f(x) with y.
Step 2: switch x and y
3: Isolate y
4: Switch the variables back
5: Replace y with f^-1(x)
6. Plug in six for the new equation where x is. :D

Answer 4

I don't know if I made it look right, but this is how it's supposed to look.
f(x)=0.3(4)^x
1. y=0.3(4)^x
2.x=0.3(4)^y
x/0.3=4^y
log(base)4 x/0.3=log(base)4 4^y
log(base)4 x/0.3=y
f^-1(x)=log(base)4 x/0.3
3. Now plug in 6 for x.
f^-1(x)=log(base)4 (6/0.3)
f^-1(x)=log(base)4 (20)
Now, solve with the change of base formula. log20/log4
Answer is roughly 2.161 (: