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The tables below show some inputs and outputs of functions 
g and 
h.





x
1
4
9
16
25
36



g(x)
1
2
3
4
5
6









x
5
10
15
20
25
30



h(x)
1
2
3
4
5
6




Evaluate.

(h@g)(25)=

◻

The tables below show some inputs and outputs of functions \newlineg and \newlineh.\newline\begin{array}{c|c} x & g(x) \ \hline 1 & 1 \ 4 & 2 \ 9 & 3 \ 16 & 4 \ 25 & 5 \ 36 & 6 \ \end{array}\newline\begin{array}{c|c} x & h(x) \ \hline 5 & 1 \ 10 & 2 \ 15 & 3 \ 20 & 4 \ 25 & 5 \ 30 & 6 \ \end{array}\newlineEvaluate.\newline(hg)(25)=(h \circ g)(25) = \newline

Full solution

Q. The tables below show some inputs and outputs of functions \newlineg and \newlineh.\newline\begin{array}{c|c} x & g(x) \ \hline 1 & 1 \ 4 & 2 \ 9 & 3 \ 16 & 4 \ 25 & 5 \ 36 & 6 \ \end{array}\newline\begin{array}{c|c} x & h(x) \ \hline 5 & 1 \ 10 & 2 \ 15 & 3 \ 20 & 4 \ 25 & 5 \ 30 & 6 \ \end{array}\newlineEvaluate.\newline(hg)(25)=(h \circ g)(25) = \newline
  1. Find g(25)g(25): First, find g(25)g(25) using the table for g(x)g(x). g(25)=5g(25) = 5
  2. Find h(g(25))h(g(25)): Next, use the value of g(25)g(25) to find h(g(25))h(g(25)). h(g(25))=h(5)h(g(25)) = h(5)
  3. Find h(5)h(5): Now, find h(5)h(5) using the table for h(x)h(x). h(5)=1h(5) = 1

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