answer:
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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