If and . Find the value of x for which . Also obtain an expression for and hence determine .

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Given that and

Let’s for the value of x for which

We need to first find the inverse of , which is given as . The inverse function undoes the original function. In this case, we have

To find , we swap and and solve for :

Solve for y, which is the inverse of function:

Divide both sides by 4

Thus,

To find , we substitute g(x) into

Since , we set the above equal to 8 and then solve for x

Cross multiplying

Divide both sides by 2

the value of x for which is 18

Next, to obtain an expression for gof and determine gof(z), we substitute f(x) into g(x), so we can then determine gof(z).

Obtaining an expression for gof(x)

To determine , we simply substitute z for x