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

1. anonymous

Does g(f(x))=x?

2. anonymous

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

3. jim_thompson5910

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

4. anonymous

So that is a yes?

5. jim_thompson5910

you tell me

6. anonymous

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

7. jim_thompson5910

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

8. jim_thompson5910

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

9. anonymous

Thanks.