Final answer:
To solve for f(g(x)) and g(f(x)), substitute g(x) into f(x) and f(x) into g(x), respectively. The result is f(g(x)) = -5x - 7 and g(f(x)) = -5x + 35.
Step-by-step explanation:
To find f(g(x)) and g(f(x)), we will substitute one function into the other. First, we are given f(x) = x - 7 and g(x) = -5x. To compute f(g(x)), we replace every occurrence of x in the definition of f with g(x), and to compute g(f(x)), we replace x in g with f(x).
For f(g(x)):
f(g(x)) = f(-5x) = (-5x) - 7 = -5x - 7.
And for g(f(x)):
g(f(x)) = g(x - 7) = -5(x - 7) = -5x + 35.
Therefore, f(g(x)) = -5x - 7 and g(f(x)) = -5x + 35.