HELP WITH FUNCTIONS!!!

[smitty0405]

I am preparing for my entrance test on Tuesday. I am having a hard time finding the information to understand functions. I am using a pre test, so I know the answers, but I am not sure how to get the right answer.

The first question list tables of values. It asks what is g(f(3))?

X F(x) X G(x)
-5 7 -2 3
-2 -5 1 -1
1 3 2 -3
3 2 3 -5

I know the answer is -3. Is that because -3 is in the same place on the table as 3?



The other question. If f(x)=2^x which yields the greatest value for f(g(x))if c>1 and x>1?

The answer is g(x)=log c x (c is subscript)

How would I know this?

Thank you.

 

[Deleted member 4993]

I am preparing for my entrance test on Tuesday. I am having a hard time finding the information to understand functions. I am using a pre test, so I know the answers, but I am not sure how to get the right answer.

The first question list tables of values. It asks what is g(f(3))?

X      F(x)                    X            G(x)
-5     7                        -2           3
-2     -5                      1            -1
1      3                        2           -3
3      2                        3           -5      
[\code]
I know the answer is -3.  Is that because -3 is in the same place on the table as 3?

[color=#FF0000] f(3) = 2 ? g[f(3)]  = g[2] = ??[/color]

The other question.  If f(x)=2^x which yields the greatest value for f(g(x))if c>1 and x>1?

The answer is g(x)=log c x  (c is subscript)

How would I know this?  

Thank you.[/quote]

 

[soroban]

Hello, smitty0405!

The first question lists two tables of values.

. . \(\displaystyle \begin{array}{c|c} x & f(x) \\ \hline \text{-}5 & 7 \\ \text{-}2 & \text{-}5 \\ 1 & 3 \\ 3 & 2 \end{array}\)

. . \(\displaystyle \begin{array}{c|c} x & g(x) \\ \hline \text{-}2 & 3 \\ 1 & \text{-}1 \\ 2 & \text{-}3 \\ 3 & \text{-}5 \end{array}\)

\(\displaystyle \text{Find }g(f(3))\)

\(\displaystyle \text{We want: }\:g(f(3))\)


\(\displaystyle \text{From the first table: }\:f(3) = 2\)

. . \(\displaystyle \text{So we have: }\:g(2)\)


\(\displaystyle \text{From the second table: }\:g(2) = -3\)

. . \(\displaystyle \text{Therefore: }\:g(f(3)) \;=\;-3\)