## mathcalculus 2 years ago For the following functions, f and g, determine (a) f(g(x)) (b) g(f(x)) If f(x)= 7x+4 and g(x)-10x+6 , then (a) f(g(x)) (b) g(f(x))

1. mathcalculus

help :(

2. satellite73

it is \(g(x)=10x+6\) ?

3. mathcalculus

-10x + 6

4. satellite73

ok

5. mathcalculus

would you be able to help me with this problem?

6. satellite73

\[f(g(x))=f(-10x+6)=7(-10x+6)+4\] then some algebra to clean up the answer

7. satellite73

you got this?

8. mathcalculus

oh so basically we plug them in together equaling to each other?

9. satellite73

oh no not equal to each other

10. mathcalculus

okay from the basic algebra how do we find f(g(x))?

11. satellite73

look at the steps i wrote first i wrote \(f(g(x))\) then i replaced \(g(x)\) by your \(g(x)\) namely \(-10x+7\)

12. mathcalculus

so I got this: -70X + 46 = -70X-40

13. satellite73

then evaluate the function \(f\) replacing \(x\) by \(-10x+7\)

14. satellite73

there is no equation to solve here

15. mathcalculus

-10x+6

16. satellite73

the solution is \[f(g(x))=f(-10x+6)=7(-10x+6)+4=-70x+42+4=-70x+46\]

17. mathcalculus

right... -70x + ......

18. mathcalculus

I did the exact same thing. Am i missing something here?

19. mathcalculus

-70x +46 ....right