Question

find f(g(x)) and g(f(x)) and determine wether the pair of functions f and g are inverse of each other.

f(x)=8x+8 and g(x)=x-8/8

f(g(x))=

Answer 1

\[f(x)=8x+8, g(x)=\frac{x-8}{8}\]
\[f(g(x))=f(\frac{x-8}{8})=8(\frac{x-8}{8})+8=x-8+8=x+0=x\]
\[g(f(x))=g(8x+8)=\frac{(8x+8)-8}{8}=\frac{8x}{8}=x\]
f and g are inverses of each other

Answer 2

You do the "inside first" so you the value of g(x) into the function (f(x)

And vice versa for the other one.

Do you understand?

Answer 3

you can also try it with numbers to get an idea of what is going on
\[f(2)=8\times 2+8=16+8=24\]
\[g(24)=\frac{24-8}{8}=\frac{16}{8}=2\]

Answer 4

any questions?

Answer 5

so if f sends 2 to 24, g sends 24 to 2 and do on

Answer 6

x is a number lol

Answer 7

well you could try it with
\[\pi\]

Answer 8

or \[e^\pi\]

Answer 9

show off

Answer 10

btw you know from elementary algebra that if you want to solve
\[8x+8=24\] for x, you would do the following steps:
a) subtract 8
b) divide by 2

that is what the inverse function says to do