Question

Which function below is the inverse of f(x) = x2 − 25?

Answer 1

f(x) = x² - 25
y = x² - 25
x = y² - 25
+ 25 + 25
x + 25 = y²
√x + 25 = √y²
±√x + 25 = y
±√x + 25 = f⁻¹(x)

Answer 2

`f(x) = x^(2) - 25`
Let f(x) = y
thus y =
`x^(2) - 25`
switch the position of y and x in the equation

`x = y ^(2) - 25`
then solve for y in this case

`x + 25 = y^(2)`
∴ y=
`√(x + 25)`

Thus,
`f^(-1) (x) = √(x + 25)`