Question

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

• A. x-2
• B. (x+2)²
• C. x³
• D. x³+2
• E. (x-2)³

Answer 1

The correct option is D x³+2

Option (d)

a) Assuming a value for x. let x=0. then $f\left(x\right)=(-2{)}^{\frac{1}{3}}$

b) Substitute, $x=(-2{)}^{\frac{1}{3}}$ in the answer options and see where you get f(x)=0

substituting, only option (d) gives $f\left(x\right)=0atx=(-2{)}^{\frac{1}{3}}$

2nd method : Let $y=(x-2{)}^{\frac{1}{3}}$

$y^3=x-2$

$y^3+3=x$

Now, replace y to x.

$f(x{)}^{-1}=x^3+3$