Question

let f(x)=4x+7 and g(x)=-2x-6. find (f o g)(4) .. show work please.. medal

Answer 1

f (g(x) ) is f(x) where x=g(x)

4(-2x-6)+7
-8x-24+7
-8x-17

-8(4)-17 = -49

-----------------------------

g(4) = -2(4)-6= -14

f(-14) = 4(-14)+7 = -49

Answer 2

Either way works

Answer 3

this is the same thing but a little more complicated. when you see (f o g) it means f(g(x)) so instead the g(x) is replacing the x in f(x)

so you have:
f(x)=4x+7

now you replace the x with g(x). so in every x in the equation you will put the g(x) equation in. it will now look like this
f(g(x))=4(-2x-6)+7

you then simplify it by multiplying 4 to (-2x-6) then simplify the equation
4(-2x-6)+7
-8x-24+7 (remember add like terms)
-8x-17

there you have the simplified form of f(g(x)) but you are not done remember it asked for (f o g)(4). when you see the 4 at the end don't let that worry you because (f o g)(4) is the same as if written f(g(4)) where g(x) is 4. so you take the g(4) and plug it back into the the simplified form you found earlier:
-8x-17
-8(4)-17
-32-17

the final answer is then:
-49

you also could solve for g(x) first and then take that answer and then plug that into the f(x) and solve. that might be another way you can try doing so you know how to do both ways.

hopefully that helped.