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e-lub [12.9K]
2 years ago
12

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

Mathematics
2 answers:
timofeeve [1]2 years ago
8 0
Answer in  2.161 tell me if i made a mistake.
Levart [38]2 years ago
5 0
<h2>Answer:</h2>

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

                f^{-1}(6)=2.161

<h2>Step-by-step explanation:</h2>

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

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