Question

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

Answer 1

Answer:

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

Step-by-step 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

$\sqrt{y^2}=\sqrt{x+3}\\y=\pm \sqrt{x+3}$

Now replace y with $f^{-1}(x)$

$f^{-1}(x)=\pm \sqrt{x+3}$

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