Question

Find (g*h)(x) and (h*g)(x) Show work please!! :D
29. g(x) = 4x
h(x) = 2x - 1

30. g(x) = -5x
h(x) = -3x + 1

31. g(x) = x + 2
h(x) = x^2

Answer 1

That circle thing means that you replace x in the function to the left with the function to the right.
So (g*h)(x) where g(x) = 4x and h(x) = 2x - 1 would be 4(2x-1). Simplifying, the answer is 8x-4.

Answer 2

(h*g)(x)=2(4x)-1=8x-1

Answer 3

Can you help me get started on 29 and 31

Answer 4

@ArkGoLucky

Answer 5

I just did 29

Answer 6

can you do 30

Answer 7

These are basically composite functions,or a function in another function.

29. If g(x) = 4x and h(x) = 2x - 1 Then:
g(h(x)) = 4(2x-1)
= 8x - 4

h(g(x)) = 2(4x) - 1
= 8x - 1

30. g(x) = -5x and h(x) = -3x + 1 Then:
g(h(x)) = -5(-3x + 1)
= 15x - 5

h(g(x)) = -3(-5x) + 1
= 15x + 1

31. g(x) = x + 2 and h(x) = x^2 Then:
g(h(x)) = (x^2) + 2
= x^2 + 2

h(g(x)) = (x+2)^2
= x^2 + 4x + 4

Answer 8

(g*h)(x)=-5(-3x+1)=15x-5
(h*g)(x)=-3(-5x)+1=15x+1

Answer 9

31.
(g*h)(x)=x^2+2
(h*g)(x)=(x+2)^2= x^2+4x+4

Answer 10

@genius12 are those the answers

Answer 11

Yes they are.

Answer 12

@genius12 There are 3 more, but are totally different from this

Answer 13

Remember you always do the same thing. When you know 2 functions, f(x) and g(x), then their composite will be f(g(x)) or g(f(x)). This just means that within that function, wherever the variable x is, then that variable will be replaced with the function f(x) or g(x). For example, if I have 2 functions f(x) = x^2 - cos(x) and g(x) = 3x - 5, then when I do f(g(x)), I just replace that x value with the function g(x).

Before, f(x) by itself looks like this: f(x) = x^2 - cos(x)
But now in the composite function f(g(x)), we have replaced 'x' with 'g(x)', so whereever there was x in the function, we now replace that with g(x), so it looks like this:

f(g(x)) = (3x-5)^2 - cos(3x-5) ---> As you can see, where-ever there was an x in f(x), that x has now been replaced by 3x - 5 in f(g(x)). And since g(x) = 3x-5 then, f(g(x)) is the same as f(3x-5). So now instead of writing f(x), we have replaced the x with g(x) so that the composite function becomes f(3x-5) and so the original function which was f(x) = x^2 - cos(x) becomes f(g(x)) = f(3x-5) = (3x-5)^2 - cos(3x-5) because I replace all the x's with 3x-5.

If you understand this basic concept, then no matter what the functions are, you should be able to make the composite functions quite easily.

Answer 14

@Firejay5

Answer 15

@Firejay5 Read what I wrote above and try to understand it.