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[tex]f(x) = 16 + \sqrt[3]{x} \\ f {}^{ - 1} (x) = [/tex]Inverse function

Sagot :

Answer:

[tex]f^{-1}(x)=(x-16)^3[/tex]

Explanation:

to find the inverse function, we have to solve for x.

First we subtract 16 from both sides to get

[tex]f(x)-16=\sqrt[3]{x}[/tex]

Then raising both sides to the power of 3 gives

[tex](f(x)-16)^3=(\sqrt[3]{x})^3[/tex][tex]x=(f(x)-16)^3[/tex]

The above we can write as

[tex]f^{-1}(^{}x)=(x-16)^3[/tex]

because we have solved for x ( thus it has become an inverse function) which is now a function of what was previously f(x).

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