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

f ( x ) = 2 x + 3
g ( x ) = x²
Part 1 : f ( g ( x )) = f ( x² ) = 2 x² + 3
Part 2 : g ( f ( x ) ) = g ( 2 x + 3 ) = ( 2 x + 3 )² = 4 x² + 12 x + 9
Part 3:
Both parts represent the composition of functions. In the first part we are plugging function x² into f ( x ) and in the second part we are plugging
2 x + 3 into g ( x ).