Question

For the functions f(x)=6x-4 and g(x)=2x²+5, find (g°f)(x).

Answer 1

To find (g\u00b0f)(x), substitute f(x) into g(x). The result after simplification is (g\u00b0f)(x) = 72x² - 96x + 37.

Step-by-step explanation:

The question asks to find the composition of two functions, (g\u00b0f)(x), where f(x) = 6x - 4 and g(x) = 2x² + 5. To find the composition (g\u00b0f)(x), we substitute the function f(x) into g(x). This means we replace every instance of x in g(x) with f(x).

First, calculate f(x):

• f(x) = 6x - 4

Now, substitute f(x) into g(x):

• g(f(x)) = 2(6x - 4)² + 5

Expand and simplify:

• g(f(x)) = 2(36x² - 48x + 16) + 5
• g(f(x)) = 72x² - 96x + 32 + 5
• g(f(x)) = 72x² - 96x + 37

Therefore, the composition of g composed with f, denoted as (g\u00b0f)(x), is 72x² - 96x + 37.