Question

Given the function

f(x)=0.3(4)x
what is the value of
f−1(6)

a. 0.360
b. 1.242
c. 2.161
d. 2.312

Answer 1

f(x)=0.3(4)^x

f^-1(x) = ?

x = 0.3(4)^y

4^y = x/0.3

4^y = 6/0.3

4^y = 20

y = 2.161

Answer 2

For this case we have the following function:

`f (x) = 0.3 (4) ^ x`
Rewriting we have:

`y = 0.3 (4) ^ x`
From here, we clear the value of x:

`(4) ^ x = y / 0.3 log4 ((4) ^ x) = log4 (y / 0.3)`
Rewriting we have:

`x = log4 (y / 0.3)`
Therefore, the inverse function is given by:

`f ^ {-1} (x) = log4 (x / 0.3)`
For x = 6 we have:

`f ^ {-1} (6) = log4 (6/0.3) f ^ {-1} (6) = 2.161`
Answer:
is the value of f^-1(6) is:
c. 2.161