Question

Given f(x) = 2x - 5 and g(x) = 3x + 4, solve for (gof)(x).

Answer 1

The composition of functions (g \circ f)(x) involves substituting f(x) into g(x). Simplifying g(f(x)) = 3(2x - 5) + 4 gives (g \circ f)(x) = 6x - 11.

Step-by-step explanation:

The student has asked to solve for (g \circ f)(x), which means to find the composition of the functions f(x) and g(x). To solve for the composition (g \circ f)(x), we need to substitute f(x) into g(x).

1. First, we have f(x) = 2x - 5.
2. Next, we substitute f(x) into g(x), yielding g(f(x)) = 3(2x - 5) + 4.
3. Simplify the expression to get g(f(x)) = 6x - 15 + 4.
4. The simplified form of g(f(x)) is 6x - 11.

Therefore, (g \circ f)(x) = 6x - 11.