Question

Given that f(x) = 3x²- 5x-1, g(x) = 4x - 2, and h(x) = 6x – 4 find each function.

1) (f. h)(x)= 18x³- 42x² + 14x +4
2)(f. h)(x)=9x+42x²+24x+14

Answer 1

To find (f∙h)(x), we substitute h(x) into f(x) and expand and simplify the expression.

Step-by-step explanation:

To find (f∙h)(x), we need to substitute the function h(x) into f(x). So, we replace every occurrence of x in f(x) with h(x).

Given: f(x) = 3x² - 5x - 1 and h(x) = 6x - 4

Substituting h(x) into f(x), we get:

(f∙h)(x) = 3(6x - 4)² - 5(6x - 4) - 1

Expanding and simplifying, we have:

(f∙h)(x) = 3(36x² - 48x + 16) - 30x + 20 - 1

(f∙h)(x) = 108x² - 144x + 48 - 30x + 20 - 1

(f∙h)(x) = 108x² - 174x + 67