Question

Find the inverse of the function.

f(x)=√x+6
Write your answer in the form a(bx+c)²+d , where a, b, c, and d are constants. Enter the domain of the inverse in the form: x≤ # or x≥ #. Simplify any fractions. f⁻¹(x)=

Answer 1

To find the inverse of the function f(x) = √x+6, swap x and y, square both sides of the equation, then solve for y. The inverse function is f⁻¹(x) = x^2 - 6. The domain of the inverse is x ≥ -6.

Step-by-step explanation:

To find the inverse of the function f(x) = √x+6, we start by replacing f(x) with y:

y = √x+6

Next, we swap x and y:

x = √y+6

Square both sides of the equation:

x^2 = y+6

Subtract 6 from both sides:

x^2 - 6 = y

Now we can write the inverse function in the form a(bx+c)²+d:

f⁻¹(x) = (x^2 - 6)

The domain of the inverse function is x ≥ -6.