Question

G(x) = 2x² and h(x) = √x²+1 .What is (goh)⁻¹ and is it a function?

Answer 1

To find (g◦h)⁻¹ and determine if it is a function, we need to first find the composition (g◦h) and then take its inverse. The inverse of (g◦h) is given by (g◦h)⁻¹(x) = √((x/2)-1). Yes, (g◦h)⁻¹ is a function.

Step-by-step explanation:

To find (g◦h)⁻¹ and determine if it is a function, we need to first find the composition (g◦h) and then take its inverse.

The composition (g◦h) means we substitute the function h(x) into the function g(x).

So, (g◦h) = g(h(x)) = 2(h(x))² = 2(√(x²+1))² = 2(x²+1).

Now, to find the inverse of (g◦h), we replace (g◦h) with y and solve the equation 2(x²+1) = y for x.

The inverse of (g◦h) is given by (g◦h)⁻¹(x) = √((x/2)-1).

Yes, (g◦h)⁻¹ is a function.