Question

If f(x) = x^2 -1, what is the equation for f–1(x)?

Answer 1

f^-1(x) = sqrt(x + 1)

Or

f^-1(x) = -sqrt(x + 1)

Explanation:

y = x² - 1

x² = y + 1

x = +/- sqrt(y + 1)

Interswitch variables:

f^-1(x) = sqrt(x + 1)

Or

f^-1(x) = -sqrt(x + 1)

Where sqrt: square root

Answer 2

The inverse is ±sqrt(x+1)

Explanation:

y = x^2 -1

Exchange x and y

x = y^2 -1

Solve for y

Add 1 for each side

x+1 = y^2-1+1

x+1 = y^2

Take the square root of each side

±sqrt(x+1) = sqrt(y^2)

±sqrt(x+1) = y

The inverse is ±sqrt(x+1)