Answer:
8x²-6x-14
Explanation:
Function Composition is applying one function to the results of another. If we apply the result of g(x) to f(x0 then it is written as f(g(x)) ans also as
(f º g) (x)
We have g(x) = - 2x + 2
f(g(x)) = f(-2x + 2)
Since f(x) = 2x² - 5x - 12, w can get f(g(x)) by simply substituting -2x + 2 wherever there is an x term in f(x) and simplifying
This is the equivalent of
f(-2x + 2)
= 2(-2x + 2)² -5(-2x + 2) - 12
(-2x + 2)² = 4x² - 8x + 4 { (a + b)² = a² + 2ab + b²}
2(-2x + 2)² = 2(4x² - 8x + 4) = 8x²-16x+8
-5(-2x + 2) = 10x - 10
So the final expression is
(8x²-16x+8) - (10x-10) - 12
= 8x² -16x + 8 - 10x + 10 -12
= 8x² - 6x -14