Let be an invertible function, then find .
Let $f(x) = 4 - (x - 7)^3$ be an invertible function, then find $f^{-1}(x)$.
Answer
Answer
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Let $y = f(x) = 4 - (x - 7)^3$.
$(x - 7)^3 = 4 - y$
$x - 7 = (4 - y)^{1/3}$
$x = 7 + (4 - y)^{1/3}$
Since $x = f^{-1}(y)$, replacing $y$ with $x$ gives:
$f^{-1}(x) = 7 + (4 - x)^{1/3}$
From ISC 2026 Mathematics Paper 1, question 3(i).