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aleksley [76]
4 years ago
8

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

Mathematics
2 answers:
sergeinik [125]4 years ago
8 0
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} } 
guapka [62]4 years ago
5 0
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!
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