Question

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

Answer 1

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

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