Question

What is the inverse of the function f(x)=19/x^3

Answer 1

step 1: replace f(x) with y ⇒ y=$\frac{19}{ x^{3} }$

step 2: switch the x and y ⇒ x=$\frac{19}{ y^{3} }$

step 3: solve for y using algebra ⇒ $xy^{3} =19$ ⇒ $y^{3}= \frac{19}{x}$ ⇒ $y= \sqrt[3]{ \frac{19}{x} }$

step 4: switch y to $f ^{-1}(x)$  and this known as "the inverse of f(x)