Given:
h is composition of two functions f and g.
[tex]h(x)=(f\circ g)(x)[/tex]
One of the function is 8x-9.
[tex]h(x)=(8x-9)^2[/tex]
To find:
The functions f(x) and g(x).
Solution:
We know that,
[tex]h(x)=(f\circ g)(x)=f[g(x)][/tex]
We have,
[tex]h(x)=(8x-9)^2[/tex]
Here, first function is 8x-9 and the second is square of it.
In [tex](f\circ g)(x)=f[g(x)][/tex], first function which is applied is g(x) and the second function is f(x).
Let [tex]g(x)=8x-9[/tex] and [tex]f(x)=x^2[/tex].
[tex]h(x)=f[8x-9][/tex]
[tex]h(x)=(8x-9)^2[/tex]
So, our assumption is correct.
Therefore, the required functions are [tex]g(x)=8x-9[/tex] and [tex]f(x)=x^2[/tex].
