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

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

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