Question

For the functions f(x) = 5x − 3 and g(x) = x + 4, which composition produces the greatest output? A. f(g(x)) produces the greatest output. B. g(f(x)) produces the greatest output. C. Both compositions produce the same output. D. Neither composition produces an output.

Answer 1

we are given with two functions f(x) = 5x − 3 and g(x) = x + 4. we are asked to evaluate f(g(x)) and g(f(x)). For the first one, f(g(x)) = 5*(x + 4) − 3 = 5x + 20 -3 = 5x + 17. For the second one, g(f(x)) = 5x − 3 + 4 = 5x + 1. when we substitute 1 to both functions, f(g(1))) = 5*1 + 17 = 22; g(f(1)) = 5*1 + 1 = 6. Hence the answer is A. f(g(x)) produces the greatest output