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. 2x^2 + 3
2.4x^2+ 9 +12x

Answer 2

2x^2+3 for first
4x^2+9+12x

Answer 3

\[f\circ(g(x))=f(g(x))=f(x^2)=2x^2+3\]
\[g(f(x))=g(2x+3)=(2x+3)^2\]

Answer 4

Are there any differences in part one and part two? If so, please explain. This is extremely important.

Answer 5

much different. first one says
1) first square,
2) then multiply by 2 and add 3

second one says
1) first multiply by 2 and add 3
2) then square the result

Answer 6

so for example if x was 10, first one would say

\[10^2=100,\text{then }2\times 100+3=203\] second one says
\[2\times 10+3=23,\text{ then } 23^2=529\] they are totally different

Answer 7

If f(x) = x + 2, find f(3).

Answer 8

????