Question

What is the composite function (fg)(x) when f(x) = 6x - 3 and g(x) = 8 - 22?

a) (fg)(x) = -140x + 66
b) (fg)(x) = -22x - 3
c) (fg)(x) = 6x - 19
d) (fg)(x) = -28x + 19

Answer 1

To find the composite function (fg)(x) for f(x) = 6x - 3 and g(x) = 8 - 22, we simplify g(x) to -14 and then substitute into f(x) to get f(g(x)) = -87. None of the answer options given match this result.

Step-by-step explanation:

To find the composite function (fg)(x) when f(x) = 6x - 3 and g(x) = 8 - 22, we first need to evaluate g(x). The function g(x) is a constant function since it does not contain the variable x, and thus g(x) simplifies to -14 after subtracting 22 from 8. Next, we substitute g(x) into f(x) to compute the composite function. Here is how we do it step by step:

First, simplify g(x): g(x) = 8 - 22 = -14.

Next, substitute g(x) into f(x): f(g(x)) = f(-14) = 6(-14) - 3.

Then, multiply 6 by -14: 6(-14) = -84.

Finally, subtract 3: -84 - 3 = -87.

Therefore, the composite function is (fg)(x) = f(g(x)) = -87, which does not match any of the options given.

Since none of the options provided matches our calculated composite function, the question as stated does not contain the correct answer.