# Homework Help: F of g of x chart

1. Jun 11, 2013

### A.J.710

Hi, I just took a placement exam for college and I would like to go over some of the questions that I got wrong. There are quite a few but this one in particular keeps me wondering. I know how to do the regular f of g of x when functions are given but in this problem it is just a chart full of numbers. Any help will be greatly appreciated.

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2. Jun 11, 2013

### gerben

Check in which column x=5 and see what f(x) is in that column, you then know what f of 5 is, now find out what the g of f of 5 is by following the same procedure as you did for finding the f of x.

3. Jun 11, 2013

### A.J.710

So the answer would be 3?

4. Jun 11, 2013

### gerben

Oh sorry, you need to find the f of g of 5 (not the g of f of 5), my original post should have been:

Check in which column x=5 and see what g(x) is in that column, you then know what g of 5 is, now find out what the f of g of 5 is by following the same procedure as you did for finding the g of x.

5. Jun 11, 2013

### A.J.710

So then -3?

6. Jun 11, 2013

### gerben

No, what is g(5)?

7. Jun 11, 2013

### A.J.710

Oh, -1? Sorry if it's wrong again I'm still a little confused on which rows to go to.

8. Jun 11, 2013

### gerben

No, to see what g(5) is, you should just check in which column x equals 5 and see what g(x) is in that column.

9. Jun 11, 2013

### MarneMath

Don't get ahead of yourself. What is g(5) based on that chart? Whatever number that is becomes your new 'x' and then find that number for f(x).

10. Jun 11, 2013

### A.J.710

So in the g column, where the 5 is, x=4. Is this the g(x) or am I still mixing it up?

11. Jun 11, 2013

### gerben

No, rows are horizontal, columns are vertical. The x row is the top row, move horizontally to where x=5, below that you see what f(x) is when x=5 and again one below you see what g(x) is when x=5

12. Jun 11, 2013

### A.J.710

Looking at the x row at the top I go to where x=5 then the f row shows -3 and the g row shows 3.

13. Jun 11, 2013

### gerben

Indeed, so f(5)=-3 and g(5)=3.

You were asked "what is f(g(5))". Now that you know what g(5) is, call it b, you can find out what f(g(5)) is. It is equal to f(b).

14. Jun 11, 2013

### A.J.710

So where the g row states 5 right above it in the f row,which is -1.

15. Jun 11, 2013

### MarneMath

Ok so can we agree that g(5) = 3, right? So now you have f(g(5)) = f(3), makes sense?

16. Jun 11, 2013

### gerben

No, when solving f(g(5)), meaning f of g of 5, you go like this:
First: What is g(5)? You saw g of 5 is 3, because when x=5 then g(x)=3.
Next: what is f(g(5))... hmm, I know g(5)=3, so the question is: "what is f(3)?"

17. Jun 11, 2013

### A.J.710

Ohhh I think I get it now! So you go back to the top afterwards so it would be 2.

18. Jun 11, 2013

### gerben

Correct!

19. Jun 11, 2013

### A.J.710

Great! Thanks guys so much for all of the help.