If f(x) = 4 - (x - 7)3, then write f-1(x). - Vidyadip

Question

If f(x) = 4 - (x - 7)³, then write f^-1(x).

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Answer

We have,

f(x) = 4 - (x - 7)³

Let y = 4 - (x - 7)³

$\Rightarrow\ (\text{x} - 7)^3 = 4 - \text{y}$

$\Rightarrow\ \text{x}-7=\sqrt[3]{4-\text{y}}$

$\Rightarrow\ \text{x}=7+\sqrt[3]{4-\text{y}}$

$\Rightarrow\ \text{f}^{-1}(\text{y})=7+\sqrt[3]{4-\text{y}}$

$\therefore\ \text{f}^{-1}(\text{x})=7+\sqrt[3]{4-\text{x}}$

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