Question

Given that f(x)=6x+5 and g(x)=2x−7, what would be the composite function (f∘g)(x)?

Answer 1

The composite function (f \circ g)(x) is found by substituting g(x) into f(x). The result, after simplification, is 12x - 37.

Step-by-step explanation:

To find the composite function (f \circ g)(x), you substitute the function g(x) into the function f(x). With the given functions f(x) = 6x + 5 and g(x) = 2x - 7, you start by evaluating g(x) and then insert that result into f(x).

1. Find g(x): This is given as 2x - 7.
2. Substitute g(x) into f(x): Replace every x in f(x) with 2x - 7 to get f(g(x)) = f(2x - 7) = 6(2x - 7) + 5.
3. Simplify the equation: Multiply out the terms 6(2x - 7) and then add 5 to get 12x - 42 + 5, which simplifies to 12x - 37.

Therefore, the composite function (f \circ g)(x) is 12x - 37.

Answer 2

f ◦ g is the composition function that has f composed with g. ... Find (f ◦ g)(x) for f and g below. f(x)=3x + 4. (6) g(x) = x2 +. 1 x. (7).

Step-by-step explanation: