Question

Someone help please thank you

Answer 1

Answer:

See below.

Step-by-step explanation:

So we have the two functions:

$f(x)=8x-5\text{ and } g(x)=9-2x$

And we want to find:

$(f\circ g)(x)\text{ and } (g\circ f)(x)$

1)

Recall that:

$(f\circ g)(x)$

is the same as:

$=f(g(x))$

Thus, we can substitute g(x):

$=f(9-2x)$

And substitute that into f(x):

$f(x)=8x-5\\f(9-2x)=8(9-2x)-5$

Distribute:

$=72-16x-5$

Subtract and simplify:

$=67-16x\\=-16x+67$

Thus:

$(f\circ g)(x)=-16x+67$

2)

Similarly:

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

Substitute f(x):

$g(f(x))=g(8x-5)$

Substitute:

$g(8x-5)=9-2(8x-5)$

Distribute:

$=9-16x+10$

Simplify:

$=-16x+19$

Therefore:

$(g\circ f)(x)=-16x+19$