Question

2.
Which of the functions below is an inverse of the quadratic function f(x) = x2 - 3 ?

Answer 1

the inverse of the quadratic function
`f(x) = x^2 - 3` is
`\mathbf{f^(-1)(x)=\pm √(x+3)}`

Explanation:

We need to find inverse of the quadratic function
`f(x) = x^2 - 3`

Let

`y=x^2-3`

Replace x and y

`x=y^2-3`

Now, we will solve for y

Adding 3 on both sides

`x+3=y^2-3+3`

`x+3=y^2`

Taking square root on both sides

`√(y^2)=√(x+3)\\y=\pm √(x+3)`

Now replace y with
`f^(-1)(x)`

`f^(-1)(x)=\pm √(x+3)`

So, the inverse of the quadratic function
`f(x) = x^2 - 3` is
`\mathbf{f^(-1)(x)=\pm √(x+3)}`