Question

Let f(x) = 2x+3 and g(x) = x2.

Part 1 Find f(g(x))
Part 2 Find g(f(x))
Part 3 Use complete sentences to explain any difference in part 1 and part 2.

Answer 1

1.Value of f(x) = 2x + 3
Value of g(x) = x^2
Putting the value of g(x) into f(x):
f(g(x)) = 2(g(x)) + 3
f(g(x)) = 2(x^2) + 3
f(g(x)) = 2x^2 + 3

2. Value of f(x) = 2x + 3
Value of g(x) = x^2
Putting the value of f(x) into g(x):
g(f(x)) =[ 2x^2 + 3 ]^2
g(f(x)) = 4x^2 + 12x + 9

3.The main difference is which term is substituted for the x. f(g(x)) means substitute the entire expression g(x) for every variable x in the expression f(x), and ,g(f(x)) means substitute the entire expression f(x) for every variable x in the expression g(x)....