Find (f g) (x) for the following f (x) = -12x^3+19x^2 - 5 g (x) = 7x^2+15

The answer to your question is (f°g) (x) = - 5856x⁶ - 25529x⁴ - 52710x² - 36220

Step-by-step explanation:

Data

f (x) = - 12x³ + 19x² - 5

g (x) = 7x² + 15

find (f°g) (x)

Process

1. - Substitute g (x) in all the x of f (x)

(f°g) (x) = - 12 (7x² + 15) ³ + 19 (7x² + 15) ² - 5

-Expand

(f°g) (x) = - 12[4913x⁶ + 2205x⁴ + 4725x² + 3375] + 19 (49x⁴ + 210x² + 225) - 5

-Simplify

(f°g) (x) = - 58956x⁶ - 26460x⁴ - 56700x² - 40500 + 931x⁴ + 3990x² + 4275 -

5

-Result

(f°g) (x) = - 5856x⁶ - 25529x⁴ - 52710x² - 36220