How do you find the inverse of $x^2 +3$ and is it a function?

Question

15024 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-30T20:33:55

$f^(-1)(x)=sqrt(x-3)$

Using the Vertical Line Test, $x^2+3$ and its inverse are functions

We know $x^2+3$ is a quadratic, which graphs as a parabola, which we know passes the Vertical Line Test. This is what makes it a function.

We essentially have

$y=x^2+3$

And the first step in finding the inverse of this function is switching $y$ and $x$ . We now have

$x=y^2+3$

Now, we solve for $y$ . Let's subtract $3$ from both sides to get

$x-3=y^2$

Taking the square root of both sides, we get

$y=sqrt(x-3)$

Since we solved for $y$ , we have found our inverse. This is also equal to

$f^(-1)(x)=sqrt(x-3)$

Where $f^(-1)(x)$ means "inverse".

The base function of our inverse is $sqrtx$ , which we also know it is a function from its graph (passes VLT).

Hope this helps!

How do you find the inverse of x^2 +3x^2 +3 and is it a function?