Perform the requested operation or operations. (5 points)

f(x) =(x-3)/8 ; g(x) = 8x + 3, find g(f(x)).

Question

Perform the requested operation or operations. (5 points)

f(x) =(x-3)/8  ; g(x) = 8x + 3, find g(f(x)).

anonymous · Answer

Does g(f(x))=x?

anonymous · Answer

probably 
one says multiply by 8, then add 3
the other says subtract 3, then divide by 8
so one undoes the other

jim_thompson5910 · Answer

$$\Large \color{red}{f(x) = \frac{x-3}{8}}$$

$$\Large g(x) = 8x+3$$

$$\Large g(x) = 8(x)+3$$

$$\Large g( \color{red}{f(x)}) = 8( \color{red}{f(x)})+3$$

$$\Large g( \color{red}{f(x)}) = 8\left( \color{red}{\frac{x-3}{8}}\right)+3$$

I'll let you simplify.

anonymous · Answer

So that is a yes?

jim_thompson5910 · Answer

you tell me

anonymous · Answer

8s cancel each other out, and the the 3s do as well

jim_thompson5910 · Answer

yes, $\LARGE 8\left(\frac{x-3}{8}\right) + 3$ simplifies to x

jim_thompson5910 · Answer

You'll also find that f(g(x)) = x as well. That means f(x) and g(x) are inverses of one another.

anonymous · Answer

Thanks.