Question

Given: F(x) = 3x^2+1, G(x) = 2x - 3, H(x) = xG^-1(x)=

Answer 1

According to the definition of the inverse function,

`\begin{gathered} G^(-1)(G(x))=x \\ \text{and} \\ G^{}(G^(-1)(x))=x \end{gathered}`

Therefore,

`\Rightarrow G^(-1)(2x-3)=x`

We need to construct G^-1(x) in such a way that when evaluated at 2x-3 the result is x.

Procedure:

1. Add +3 so that we transform 2x-3 into 2x

2. Multiply by 1/2 so that from 2x we get x

Algebraically,

`((2x-3)+3)/(2)=x`

Then, G^-1(x) is

`\Rightarrow G^(-1)(x)=(x+3)/(2)`

The answer is G^-1(x)=(x+3)/2