Find [g *h](x) and [h*g](x) . g(x) = 5x h(x) = –10x3 + 13x2 – 3x + 3
[g *h](x)= –50x3 + 65x2 – 15x + 15
[h*g](x) = –1250x3 + 325x2 – 15x + 15
[g *h](x) = –50x4 + 65x3 – 15x2 + 15x
[g *h](x) = –1250x4 + 325x3 – 15x2 + 3x
[g *h](x) = –50x3 + 65x2 – 15x + 15
[h*g](x) = –1250x3 + 325x2 – 15x + 3
[g *h](x) = 50x3 + 65x2 – 15x + 15
[h*g](x) = –1250x3 + 325x2 – 15x + 3

(g ο h)(x) = -50x³ + 65x² - 15x + 15

(h ο g)(x) = -1250x³ + 325x² - 15x + 3 ⇒ 3rd answer

Step-by-step explanation:

* Lets explain the composite function

- A composite function is a function that depends on another function

- A composite function is created when one function is substituted into

another function  

- Example:

# (f ο g)(x) is the composite function that is formed when g(x) is  

 substituted for x in f(x).

* Now lets solve the problem

∵ g(x) = 5x

∵ h(x) = -10x³ + 13x² - 3x + 3

- To find (g ο h)(x) replace x in g by h(x)

∴ Replace x by -10x³ + 13x² - 3x + 3

∴ (g ο h)(x) = 5(-10x³ + 13x² - 3x + 3)

∴ (g ο h)(x) = -50x³ + 65x² - 15x + 15

- To find (h ο g)(x) replace each x in -10x³ + 13x² - 3x + 3  by g(x)

∴ Replace each x in -10x³ + 13x² - 3x + 3 by 5x

∴ (h ο g)(x) = -10(5x)³ + 13(5x)² - 3(5x) + 3)

∴ (h ο g)(x) = -10(125x³) + 13(25x²) - 15x + 3

∴ (h ο g)(x) = -1250x³ + 325x² - 15x + 3

* (g ο h)(x) = -50x³ + 65x² - 15x + 15

 (h ο g)(x) = -1250x³ + 325x² - 15x + 3

-1, -2, -3, -4, -6

step-by-step explanation:

answer: a and b

step-by-step explanation: