Question

What is the inverse of this function?

f(x)=√x
+ 3, x ≥ − 3
f-¹(x) =
x²-
-
for x ≤

Answer 1

4, 3, 0

Explanation:

Let f(y)=x.

`x=-(1)/(2)√(y+3) \\ \\ -2x=√(y+3) \\ \\ 4x^2=y+3 \\ \\ y=f^(-1)(x)=\boxed{4}x^2-\boxed{3}`

The domain of the inverse is the same as the range of the original function. For the original function, we know that it is decreasing, so the range is

`y\leq -(1)/(2)√(-3+3)=0`

and hence the domain of our inverse is

`x \leq 0`