Question

The one-to-one functions g and h are defined as follows.g(x) = 4x - 3h={(-6, 3), (-4, 7), (3, -8), (6, 4)Find the following

Answer 1

It is given that

$g(x)=4x-3$

Now to find the inverse of g

Let

$\begin{gathered} y=4x-3 \\ 4x=y+3 \\ x=\frac{y+3}{4} \end{gathered}$

So

$g^{-1}(x)=\frac{x+3}{4}$

Now we know that

$(g^{-1}.g)(x)=\text{ x}$

So

$(g^{-1}.g)(2)=2$

And since

$h(-6)=3$

So

$h^{-1}(3)=-6$