Question

What is the inverse of f(x)= cube root of x +2.

Answer 1

f(x)=$\sqrt[3]{x+2}$
to solve for the inverse of a function you do 4 steps:
1. subsitute f(x) with y
2. switch y and x places
3. solve for y
4. subsitute y with f⁻¹(x)

so we have
f(x)=$\sqrt[3]{x+2}$
subsitute f(x) with y
y=$\sqrt[3]{x+2}$
switch x and y
x=$\sqrt[3]{y+2}$
solve for y

x=$\sqrt[3]{y+2}$
cube both sides
$x^{3}$=y+2
subtract 2 from both sides
$x^{3}-2$=y

subsitute y with f⁻¹(x)
f⁻¹(x)=$x^{3}-2$



the answer is f⁻¹(x)=$x^{3}-2$