Question:
If $f(x)=4-(x-7)^{3}$, then write $f^{-1}(x)$. [NCERT EXEMPLAR]
Solution:
We have,
$f(x)=4-(x-7)^{3}$
Let $y=4-(x-7)^{3}$
$\Rightarrow(x-7)^{3}=4-y$
$\Rightarrow x-7=\sqrt[3]{4-y}$
$\Rightarrow x=7+\sqrt[3]{4-y}$
$\Rightarrow f^{-1}(y)=7+\sqrt[3]{4-y}$
$\therefore f^{-1}(x)=7+\sqrt[3]{4-x}$
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