Solving a F of g of x Chart Placement Exam Question

[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.

 

[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.

 

[A.J.710]

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.

So the answer would be 3?

 

[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.

 

[A.J.710]

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.

So then -3?

 

[gerben]

No, what is g(5)?

 

[A.J.710]

No, what is g(5)?

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

 

[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.

 

[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).

 

[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?

 

[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

 

[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.

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

 

[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).

 

[A.J.710]

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).

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

 

[MarneMath]

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

 

[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)?"

 

[A.J.710]

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

 

[gerben]

Correct!

 

[A.J.710]

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