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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