Question

Find the inverse of the function. Is the inverse a function? f(x) = (x − 2)2

Answer 1

`f^(-1)(x)=√(x)+2`

Explanation:

Given function is,

f(x) = (x - 2)²

Step - 1

Rewrite the function in the form of a equation.

y = (x - 2)²

Step - 2

Interchange the variables 'x' and 'y',

x = (y - 2)²

Step - 3

Solve the equation for y,

x = (y - 2)²

y - 2 = √x

y = 2 + √x

Step - 4

Rewrite the equation in the form of a function,

`f^(-1)(x)=√(x)+2`