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)=\(x^{3}-2\)
