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

Answer:

The value of $f^{-1}(6)$ is:

                $f^{-1}(6)=2.161$

Step-by-step 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.

$0.3(4)^x=6\\\\i.e.\\\\4^x=\dfrac{6}{0.3}\\\\i.e.\\\\4^x=20$

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:

$x=\dfrac{\log 20}{\log 4}$

i.e.

$x=\dfrac{1.3010}{0.6021}\\\\i.e.\\\\x=2.161$

Hence, we have:

                    $f^{-1}(6)=2.161$