## anonymous one year ago Given the following functions f(x) and g(x), solve f[g(6)] and select the correct answer below: f(x) = 6x + 12 g(x) = x − 8 −96 0 24 48

1. anonymous

i will medal

2. zepdrix

Hey William :)$\large\rm \color{orangered}{f(x)=6x+12},\qquad\color{royalblue}{g(x)=x-8}$

3. zepdrix

Hmm so we need to solve this:$\large\rm \color{orangered}{f\left[\color{royalblue}{g(6)}\right]}$

4. zepdrix

We want to work from the inside and move outward. So let's deal with the blue first. What is the value of the function g, when 6 is plugged in for x?

5. anonymous

so you say to turn it into g(x)=6-8?

6. zepdrix

Good, yes.$\large\rm g(x)=x-8,\qquad g(6)=6-8$Looks like we end up with -2, ya?

7. zepdrix

So then,

8. zepdrix

That simplifies down the blue inner part for us. $\large\rm \color{orangered}{f\left[\color{royalblue}{g(6)}\right]}=\color{orangered}{f\left[\color{royalblue}{-2}\right]}$

9. zepdrix

So now all we need to do is simply plug -2 into our f function.

10. anonymous

im having trouble someone talk me through this

11. anonymous

hello?

12. anonymous

is it f(x)=6(-2) +12

13. jim_thompson5910

yes now evaluate 6(-2) + 12 and you're done

14. jdoe0001

hmmm what would you get for say $$\bf {\color{brown}{ g(6)}}?$$

15. anonymous

0

16. jdoe0001

0? how.. did you get 0 though?

17. jdoe0001

anyhow $$\bf g(x)=x-8\qquad g({\color{brown}{ 6}})={\color{brown}{ 6}}-8$$

18. anonymous

|dw:1438904530281:dw|

19. jdoe0001

hmmm ok... wondering where the -2 came from

20. jim_thompson5910

@jdoe0001 the -2 is from g(6) = 6-8 = -2

21. jdoe0001

hmm maybe I missed something. lemme recheck

22. jdoe0001

ohh hmm

23. jdoe0001

well, then $$\bf f(x)=6x+12\qquad f({\color{brown}{ g(6)}})=6[{\color{brown}{ g(6)}}]+12 \\ \quad \\ {\color{brown}{ g(6)}}=-2\qquad then\\\ \quad \\ f({\color{brown}{ g(6)}})=6[{\color{brown}{ g(6)}}]+12\implies f({\color{brown}{ -2}})=6[{\color{brown}{ -2}}]+12\to 0$$