Find the inverse of the function f(x)=(x−2)13

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Find the inverse of the function $f (x) = (x - 2)^{\frac{1}{3}}$

Answer: Option D
:
D

Option (d)
Let $y = (x - 2)^{\frac{1}{3}}$
$y^{3} = x - 2$
$y^{3} + 2 = x$
Now, replace y to x.
$f (x)^{- 1} = x^{3} + 2$

Alternative Approach:
a) Assuming a value for x. let x=0. then $f (x) = (- 2)^{\frac{1}{3}}$
b) Substitute, $x = (- 2)^{\frac{1}{3}}$ in the answer options and see where you get f(x)=0
substituting, only option (d) gives $f (x) = 0 a t x = (- 2)^{\frac{1}{3}}$

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