Question

HELP PLEASE.

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.

I don't need the whole thing done, i just want to make sure i'm doing it right.
For f(g(x)) i plugged in 2x(x^2) + 3.
is that right? and how would i solve.

Answer 1

$$
f(x) = 2x+3\\
g(x) = \color{red}{x^2}\\
f(g(x)) = 2(\color{red}{x^2})+3
$$

Answer 2

there's really nothing to solve, or even simplify, is a simplified polynomial already

Answer 3

I don't understand why it would be 2(x^2)..
What happens to the x already with the 2?
2x(x^2) ?

Answer 4

f(x) = 2x + 5(x +3)

f( a ) = 2(a) + 5( (a) + 3)

f( a + b) = 2(a + b) + 5( (a + b) + 3)

f( g(x) ) = 2( g(x) ) + 5( (g(x)) + 3)

Answer 5

so, the "x" in the HOST function, is really just a PLACEHOLDER for whatever is passed on as argument

Answer 6

got what he meant?

Answer 7

I think so. At least, i understand what to plug in and solve, not that theres much solving..

So for the third part, it's asking for the difference between them, what's the difference? I dont really see any?

Answer 8

i know they are kind of different in solving. The f(x) value replaces the x in g(x).

But does that count as a difference? @jdoe0001 @Loser66

Answer 9

yes

Answer 10

you fill in the ? marks