Answer:
See below.
Step-by-step explanation:
So we have the two functions:
[tex]f(x)=8x-5\text{ and } g(x)=9-2x[/tex]
And we want to find:
[tex](f\circ g)(x)\text{ and } (g\circ f)(x)[/tex]
1)
Recall that:
[tex](f\circ g)(x)[/tex]
is the same as:
[tex]=f(g(x))[/tex]
Thus, we can substitute g(x):
[tex]=f(9-2x)[/tex]
And substitute that into f(x):
[tex]f(x)=8x-5\\f(9-2x)=8(9-2x)-5[/tex]
Distribute:
[tex]=72-16x-5[/tex]
Subtract and simplify:
[tex]=67-16x\\=-16x+67[/tex]
Thus:
[tex](f\circ g)(x)=-16x+67[/tex]
2)
Similarly:
[tex](g\circ f)(x)=g(f(x))[/tex]
Substitute f(x):
[tex]g(f(x))=g(8x-5)[/tex]
Substitute:
[tex]g(8x-5)=9-2(8x-5)[/tex]
Distribute:
[tex]=9-16x+10[/tex]
Simplify:
[tex]=-16x+19[/tex]
Therefore:
[tex](g\circ f)(x)=-16x+19[/tex]
