Question

Which graph shows the composite function (f•g)(x)?

f(x)=-2x-5
g(x)=x-2

Answer 1

To find the composite function (f•g)(x), we need to perform the function composition by substituting g(x) into f(x).

Given:

f(x) = -2x - 5

g(x) = x - 2

To find (f•g)(x), we substitute g(x) into f(x):

(f•g)(x) = f(g(x))

Substituting g(x) into f(x):

(f•g)(x) = f(x - 2)

Now, let's simplify the expression:

Replace x in f(x) with (x - 2):

(f•g)(x) = -2(x - 2) - 5

Expand and simplify:

(f•g)(x) = -2x + 4 - 5

Combine like terms:

(f•g)(x) = -2x - 1

Therefore, the composite function (f•g)(x) is -2x - 1.

Now, to identify the corresponding graph, we look for the equation -2x - 1 among the options. The graph that represents this equation is the one that shows a linear function with a slope of -2 and a y-intercept of -1.

To summarize:

The composite function (f•g)(x) is -2x - 1. The graph that represents this composite function will show a linear function with a slope of -2 and a y-intercept of -1.

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