Forming Composite Functions - belch !!?

Question

I really can't understand this concept at all, but especially this problem. Can you not only show me how to do it, but explain why you do what you do - please ?

f(x) = 2x g(x) = x+7

(f of g)(2) = ?

Answer 1

I think you meant to split the first line into two:

f(x) = 2x
g(x) = x+7

Now, "(f of g)(2)" just means this:
1) First plug "2" into the function "g" and see what answer you get.
2) Then, plug the answer above into function "f", and see what NEW answer you get.

Step by step:

First find g(2) (pronounced, "g of 2"). This means you substitute 2 for x everywhere in the function definition.

g(x) = x + 7, so
g(2) = 2 + 7 = 9

Next, we plug that answer (9) into the "f" function. That is, we find f(9).

f(x) = 2x, so:
f(9) = 2•9 = 18.

So the final answer is:

(f of g)(2) = 18

Answer 2

ok, (f of g)(2) is the same as f(g(2))

all you do is plug the g value into the x values of f(x).
Like this......

g = x + 7
f = 2x They want f OF G which is f(g(x))

2(x+7) you plug in the g value into the x value of "f". When they give you composite functions, all you do is plug numbers in.
Ex: f(x) = 3x g(x) 2 +3x

If you want to find "f", take the g function and plug that into the x value of f. So..... 3(2+3x) this is what f(x) equals.
To find g(x), just plug in the whole equation for f(x) into the x of g(x). It will look like this........2 + 3(3x). This is what the answer to the practice would be. Don't worry about it. Honestly, I had so much trouble with this at the beginning and I though I would never understand. You can do it! don't give up your efforts. :)

Forgot to mention quick rules of thumb: When you get a fraction, remember that the denominator can never equal a zero. so eliminate all the numbers that would add up to the other that equals zero. Ex. 2/x + 3 Your eliminating number is -3 for x because you can't have a zero in the denominator. Also, for square roots, you can't have a negative in a square root or even roots such as 4th root 6throot, 8th root.....etc.
And: the inverses of the composite functions f(g(x)) or g(f(x)) always equal x. if they do not, then they are not inverses of eachother. :)

Answer 3

f(x) = x + 7
2x g(x) = x+7 or g(x) = (x+7)/(2x)
fog(x) = g(x) + 7
fog(2) = g(2) + 7 = (2+7)/(2*2) + 7 = 9/4 + 7 = 9/4 + 28/4
= 37/4
Now, see if you can do gof(x); here is how:
1. substitute f(x) into the x values of g(x)
2. now you have the function gof(x)
3. do not forget this, you are having a test on it

Answer 4

Since you are doing f of g, you need to put the g function in the f one.

f(x) = 2x
g(x) = x+7
You will put x+7 since that's g(x) into x for the f(x) function
(f of g)(x)=2(x+7)
Now solve using 2
(f of g)(2)=2(2+7)
(f of g)(2)=2*9=18
18 is your answer
Hope this helps!

Answer 5

(f of g) (2) can be written as f( g(2) ). Basically means you need to plug 2 for x in g function

g(2) = x + 7
g(2) = 2 + 7
g(2) = 9

f ( g(2) ) . We know that g(2) = 9 so, we have f (9).

you need to plug 9 for f function

f(9) = 2x
f(9) = 2(9)
f(9) = 18

so the answer is 18