Question

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

0.360

1.242

2.161

2.312

Answer 1

answer in  2.161 tell me if i made a mistake.

Answer 2

The value of
`f^(-1)(6)` is:

`f^(-1)(6)=2.161`

Explanation:

We are given a function f(x) as:

`f(x)=0.3\cdot 4^x`

Now, we are asked to find the value of:

`f^(-1)(6)`

Let:

`f^(-1)(6)=x\\\\i.e.\\\\f(x)=6`

i.e.

`0.3(4)^x=6\\\\i.e.\\\\4^x=(6)/(0.3)\\\\i.e.\\\\4^x=20`

Now, we take the logarithmic function on both the side of the inequality in order to obtain the value of x.

`x\log 4=\log 20`

( Since, we have:

`\log m^n=n\log m` )

Hence, we have:

`x=(\log 20)/(\log 4)`

i.e.

`x=(1.3010)/(0.6021)\\\\i.e.\\\\x=2.161`

Hence, we have:

`f^(-1)(6)=2.161`