Question

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Answer 1

Given:

h is composition of two functions f and g.

$h(x)=(f\circ g)(x)$

One of the function is 8x-9.

$h(x)=(8x-9)^2$

To find:

The functions f(x) and g(x).

Solution:

We know that,

$h(x)=(f\circ g)(x)=f[g(x)]$

We have,

$h(x)=(8x-9)^2$

Here, first function is 8x-9 and the second is square of it.

In $(f\circ g)(x)=f[g(x)]$, first function which is applied is g(x) and the second function is f(x).

Let $g(x)=8x-9$ and $f(x)=x^2$.

$h(x)=f[8x-9]$

$h(x)=(8x-9)^2$

So, our assumption is correct.

Therefore, the required functions are $g(x)=8x-9$ and $f(x)=x^2$.