charles: F(x) =x2 +1, g(x) =4x+4 find (fog)(x)

[fannc7]

I am a older student 69 years old I got stuck on this problem and don't know how to finish. F(x) =x² +1, g(x) =4x+4 find (fog)(x)

(x² +1) (4x +4) (fog)^(x)
fog(x) = 4x³ (4x+4)
= 16x⁴ + 4

 

[stapel]

I am a older student 69 years old I got stuck on this problem and don't know how to finish. F(x) =x² +1, g(x) =4x+4 find (fog)(x)

I have no idea what "charles" (from your subject line) might mean. I've added the stuff after the colon to clarify your subject line, and have moved your post from "News" to an appropriate category.

In your text, quoted above, are you really given the function "F" and then asked to work with "f", or is the first "F" meant to be an "f". (Mathematically, these are two different things, is why I'm asking.) I will assume that "F" means "f", so the exercise is:

. . . . .\(\displaystyle \mbox{Given }\, f(x)\, =\, x^2\, +\, 1\, \mbox{ and } g(x)\, =\, 4x\, +\, 4,\, \mbox{ find }\, (f\, \circ\, g)(x).\)

(x² +1) (4x +4) (fog)^(x)

I'm sorry, but I don't know what this means...?

fog(x) = 4x³ (4x+4)

How did you arrive at this equation?

= 16x⁴ + 4

This is not equal to your previous line. The 4x³ (even were it valid) would need to be multiplied on all of the terms inside the parenthetical, not just the first one. (here)

Are you familiar with functions and function notation? Have you studied function "composition" at all? Thank you!