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

1 Answer
May 30, 2018

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

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

Explanation:

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!