Find the inverse of f(x)=√2x−4 , if it exists.

Question

The domain of the inverse is:

Answer 1

Hello Hadassah,

I am assuming that the 2x - 4 expression is under the square root sign, f(x) = √(2x - 4). The domain of this function is [2, ∞), since the square root of a negative number is not a real number.

The range of f(x) is range is [0, ∞).This the is key to identifying the domain of the inverse function.

y = √(2x - 4) Substitute y for f(x).

x = √(2y - 4) Exchange the x and y positions, and solve for y.

x² = (2y - 4) Raise both sides of the equation to the power 2, then solve for y.

x² + 4 = 2y Add 4 to each side of the equation.

(x² + 4)/2 = y Replace the y with f^-1(x).

f^-1(x) = (x² + 4)/2 The inverse does exist and the domain of f^-1(x) is [0, ∞).

Regards,

Anita A.

Answer 2

y = √(2x-4), the inverse is found by switching the x and y, x = √(2y-4), y =(1/2)(x² + 4)