Question

what is the inverse of the function h(x) = 3x^2 - 1?

Answer 1

Hello there!

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

So, the answer is
$h ^{-1}(x)= \sqrt{3(1+x)/3$ , $- \sqrt{3(1+x)}/3$

I hope this helps!

Answer 2

There is a simple rule to find the inverse of any function:
1. Trade places between y and x (h(x) and x in this case)
2. Solve for y (h(x) in this case)
3. That's all!
Let's solve it now:
1. Trade places between h(x) and x: $x = 3(h(x))^{2} -1$
2. Solve for h(x): 
$3(h(x))^{2} = x+1 \\ (h(x))^{2} = \frac{x+1}{3} \\ h(x) = + \sqrt{ \frac{x+1}{3} } $ or $- \sqrt{ \frac{x+1}{3} }$
3. So, the inverse is system of graphs $h(x) = + \sqrt{ \frac{x+1}{3} }$ and $h(x) = - \sqrt{ \frac{x+1}{3} }$