Question

Can someone please help me with this function? The screenshot is attached it's number 2

Answer 1

Function composition can be a bit weird.

You know the definition, (fog)(x) = f(g(x)). Good.

Now, let's look at what they want. They want to go (fog)(9). You know that is just f(g(9)).

But wait! They gave you g(9). It's 11. So now you have f(11).

And look at that, they also gave us f(11). It's 22.

So, (fog)(9) = f(g(9)) = f(11) = 22.

Answer 2

They want to know** -- not go.

Answer 3

Thank you for explaining!

Answer 4

My pleasure!

Answer 5

could you explain this? I know the domain but I'm not sure what they are asking me to enter in the blank?

Answer 6

Oh uh, so they give you f(x) and g(x).

They want you to compose them. Instead of a discrete number, we're going to put in the entire expression.

so (fog)(x) = f(g(x)). Since f(x) = x^4, and g(x) = x+3, then f(g(x)) = (x+3)^4.

Similarly g(f(x)) = x^4 + 3.

It's confusing because we're using the same x for two different functions.

Let's say f is a function of the variable u. So f(u) = u^4, and g(x) = x+3.

I'm going to now let u take the value of g(x) = x + 3.

So f(g(x)) = (x+3)^4.

Answer 7

You can also think about it like this:

f is a function that takes a number and calculates it the fourth power of that number.

But what if the number that I put into f comes from another function -- in our case it can come from g(x).

Then we simply apply the "fourth power function" to the function we plugged in.

(fof)(x) = f(f(x)) says to take the function f, and apply the "fourth power function" to itself. So f(f(x)) should equal (x^4)^4 = x^16.

Answer 8

I'm not sure I understand I thought for the 2nd part it was x^4 but it was incorrect

Answer 9

x^4 +3?

Answer 10

Yes that's right because it asks for g(f(x)). Since g(x) = x+3, and f(x) = x^4, you want to replace the x's in g(x) with f(x). So g(f(x)) = x^4 + 3.

Answer 11

Thanks how about fof(x). I keep getting this one wrong

Answer 12

It's the same kind of method, except now you put in f(x) = x^4 into itself.
Like (x^4)^4. Using the rules of exponents, this equals x^16.

Answer 13

Thank you so much for your help!

Answer 14

Sorry to keep bothering you! is (gog)(x) correct?

Answer 15

Sorry for taking a while. (gog)(x) would be g(g(x)) = (x+3) + 3 = x+6.

Answer 16

No worries I just appreciate the help. I keep messing this one up

Answer 17

16x-45 or way off? ;-/

Answer 18

g(x) = 7x-4, so g(g(x)) replaces every instance of x with g(x).

So, g(g(x)) = 7 (7x-4) - 4 = 49x - 28 - 4 = 49x - 32.

Answer 19

Geez I keep mixing up the numbers. I'm going to have a lot of practice to do this weekend haha

Answer 20

Can you please please help me with one more?

Answer 21

Sorry I don't know why I'm having such a hard time with this section. Not good!

Answer 22

Oh we're multiplying functions now. I find this to be easier than composition, or at least more straight-forward.

f(x) = 9/x and g(x) = 11/(x+11).

So we multiply those fractions together, we get 99 / (x(x+11)).

Answer 23

Dividing them:
\[ \frac{\frac{9}{x}}{\frac{11}{x+11}} = \frac{9(x+11)}{11x}\]

Remember, when you divide fractions, you just multiply by the reciprocal.

Answer 24

Can the multiplication one be written as 99/x^2+11?

Answer 25

Oh yeah you can distribute the x if you want. However, you forgot to distribute it to the 11 also.
Remember a(b+c) = ab + ac.

Answer 26

99/x^2+11x?

Answer 27

Yeah like that.

Answer 28

Okay and when I'm adding those is 20x+99/x^2+11x correct?

Answer 29

Yup! You found the common denominator and distributed correctly.

Answer 30

I'm confused on the subtraction one. Last one I promise!

Answer 31

3x+99/x^2+11x I don't think I did that one right

Answer 32

Thanks for all your help! :)

Answer 33

f(x) = 0.50x
g(x) = x-65.

So f(g(x)) = 0.50 [ x - 65 ] = 0.50x - 32.5.

You were close, but 65/2 = 32.5, not 25.

Answer 34

darn! thank you soooo much for all your help! sorry if i was an annoyance! thanks again!

Answer 35

Oh it was no problem! :) Just keep practicing.