Question

Given f(x) = 10 + 3x and g(x) = -% -1, find (gof) (q - 6).

Do not enter your answer as an equation; just enter the final value or
expression without parentheses.

Answer 1

To find (g \circ f)(q - 6), we first apply f to (q - 6) to get f(q - 6) = 3q - 8 and then apply g to get g(f(q - 6)) = -3q + 7 as the simplified final expression.

Step-by-step explanation:

To solve the problem, we need to find (g \circ f)(q - 6), which means we first apply f to (q - 6) and then apply g to the result.

1. Begin with the function f(x) = 10 + 3x. Substituting (q - 6) into f, we get f(q - 6) = 10 + 3(q - 6).
2. Simplify f(q - 6) to get f(q - 6) = 10 + 3q - 18.
3. Further simplify to get f(q - 6) = 3q - 8.
4. Now apply the function g(x) = -x -1 to the result from step 3, g(3q - 8).
5. Substitute 3q - 8 into g, yielding g(3q - 8) = -(3q - 8) - 1.
6. Simplify this to get g(3q - 8) = -3q + 8 - 1.
7. The final expression is -3q + 7.