Question

Find (f∘g)(x) and (g∘f)(x). f(x)=7x−7, g(x)=4−2x

1.(f∘g)(x)=−14x−35, (g∘f)(x)=−14x+49
2.(f∘g)(x)=−14x+35, (g∘f)(x)=−14x−49
3.(f∘g)(x)=14x−35, (g∘f)(x)=14x+49
4.(f∘g)(x)=14x+35, (g∘f)(x)=14x−49

Answer 1

The composed functions (f∘g)(x) and (g∘f)(x) are 21 - 14x and 18 - 14x respectively, corresponding to option 3.To find (f∘g)(x), substitute g(x) into f(x) and simplify the expression. To find (g∘f)(x), substitute f(x) into g(x) and simplify the expression

Step-by-step explanation:

To find (f\u2218g)(x) and (g\u2218f)(x), we need to substitute the functions into each other and simplify. Given f(x)=7x-7 and g(x)=4-2x, let's begin the composition process

For (f\u2218g)(x), we substitute g(x) into f(x):

1. Calculate f(g(x)): f(4-2x) = 7(4-2x) - 7.
2. Distribute the 7: 28 - 14x - 7.
3. Simplify: 21 - 14x

For (g\u2218f)(x), we substitute f(x) into g(x):

1. Calculate g(f(x)): g(7x-7) = 4 - 2(7x-7).
2. Distribute the -2: 4 - 14x + 14.
3. simplify: 18 - 14x.

Therefore, the correct answers are: (f\u2218g)(x) = 21 - 14x and (g\u2218f)(x) = 18 - 14x, which corresponds to option 3.