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

In English, f(g(x)) means take the expression for g(x) (in your example that would be "x2") an replace every "x" in the f(x) with your g(x) expression.

Answer 2

Take f(x) = 2x + 3. Now replace the x with x2 and simplify. What do you get?

Answer 3

Assuming g(x) is x^2...

1. f(g(x)) = 2x^2 + 3
2. (2x + 3)^2 = 4x^2 + 12x + 9
3. The difference is which term is substituted for the variable x. f(g(x)) means substitute the entire expression g(x) for every variable x in the expression f(x), and vice-versa..

Answer 4

Yes its ^2 sorry about that

Answer 5

Nothign else could be done to part 1 right?

Answer 6

In part 1, just substitute x^2 for x in f(x) ... 2*(x^2) + 3 = 2x^2 + 3

Answer 7

thank you