Question

If f(x) = x-7 and g(x) = 3x+1, then (g-f)(3) is equivalent to:

A. -18
B. -20
C. -6
D. 14

Answer 1

To find (g-f)(3) for the functions f(x)=x-7 and g(x)=3x+1, you perform the operations g(3)-f(3). After substitution and arithmetic, you find that (g-f)(3) equals 14.

Step-by-step explanation:

To find the value of (g-f)(3), where f(x) = x-7 and g(x) = 3x+1, you perform the following steps:

1. First, compute f(3) by substituting 3 into f(x): f(3) = 3 - 7 = -4.
2. Next, compute g(3) by substituting 3 into g(x): g(3) = 3(3) + 1 = 9 + 1 = 10.
3. Then, subtract f(3) from g(3) to get (g-f)(3) which is g(3) - f(3) = 10 - (-4).
4. Finally, perform the subtraction: 10 - (-4) = 10 + 4 = 14. Therefore, (g-f)(3) = 14.

The correct answer to the question is D. 14.