Question

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

Part 1 [2 points] Find f(g(x))
Part 2 [2 points] Find g(f(x))
Part 3 [4 points] Use complete sentences to explain any difference in part 1 and part 2.

Answer 1

@Hero @mathmale @mathstudent55

Answer 2

f(x) = 2x + 3
g(x) = x^2
f(g(x)) = 2(g(x)) + 3

g(f(x)) = f(x)^2

Answer 3

ok thanks! can you help me on part 3? :)

Answer 4

For f(g(x)), the entire function g(x) is used as the input into f(x).
For g(f(x)), the entire function f(x) is used as the input into g(x).

Answer 5

For Part 1 and 2, You still have to figure out what

2(g(x)) + 3 is equal to
f(x)^2 is equal to

The final expression should be completely algebraic.

Answer 6

how do I figure that out?

Answer 7

Insert the original expression for g(x) into 2(g(x)) + 3 then simplify. Insert the original expression for f(x) into f(x)^2 then simplify.

Answer 8

oh so it would like this: ....