Question

What is the inverse of f(x)=x^2 - 2

Answer 1

-1

f (x) = +√(x + 2)

Explanation:

The graph of f(x)=x^2 - 2 is that of a parabola that opens up and has its vertex at (0, -2). A horizontal test line drawn through this graph intersects the graph in 2 places, which indicates that f(x)=x^2 - 2 per se does not have an inverse function.

However, if we restrict the domain of f(x)=x^2 - 2 to [0, ∞), the graph is the right half of that of f(x)=x^2 - 2. This part of the graph shows that f(x)=x^2 - 2 on [0, ∞) has an inverse.

To find this inverse algebraically:

1) replace "f(x)" with "y": y = x^2 - 2

2) interchange x and y: x = y^2 - 2

3) solve this result for y: y^2 = x + 2, or y = +√(x + 2)

4) replace this 'y' with the symbol for 'inverse function of x:'

-1

f (x) = +√(x + 2). The domain of this function is (-∞, -2].

Answer 2

`f^(-1)` (x) =
`√(x+2)` , -
`√(x+2)`

Explanation:

To find the inverse, interchange the variables and solve for y.

Hope this helps,

Davinia.