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.

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) ...