Question

If f(x) = x2 -1, what is the equation for f^–1(x)?

Answer 1

f^-1(x) means you are finding the inverse.

Answer 2

In order to find the inverse we replace f(x) with y so we get y=x^2-1

Answer 3

\(\bf f(x) ={\color{red}{ y}}= {\color{blue}{ x}}^2 -1\qquad inverse\implies {\color{blue}{ x}}= {\color{red}{ y}}^2 -1\)

solve for "y"

notice that to find the inverse "relation", we simply swap about the variables, then solve for "y"

Answer 4

Now we switch the x and y so we get x=y^2-1 and solve for y