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: