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Graph the composite function g ⁡ ( f ⁡ ( x ) ) . f ⁡ ( x ) = - 2x − 5
g(x)= x -1

User Mike Lutz
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1 Answer

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The graph of the composite function g(f(x)) can be obtained by first evaluating f(x) and then substituting that expression into g(x).

f(x) = -2x - 5

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

= (-2x - 5) - 1

= -2x - 6

Therefore, g(f(x)) = -2x - 6.

To graph this function, plot a few points:

When x = 0, g(f(0)) = -6

When x = 1, g(f(1)) = -8

When x = -1, g(f(-1)) = -4

These points can be plotted on a coordinate plane, and then connected with a straight line. The resulting graph is a line with a slope of -2 and a y-intercept of -6.

Explanation:

User Joscarsson
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