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Sagot :
Let's first solve for [tex]\(a\)[/tex] for the function [tex]\(f(x)\)[/tex].
We know that [tex]\(f\)[/tex] is an even function. By definition, even functions satisfy the following property:
[tex]\[ f(-x) = f(x) \][/tex]
Given the table for [tex]\(f(x)\)[/tex]:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline -2 & 4 \\ \hline 0 & 5 \\ \hline 2 & $a$ \\ \hline 3 & 7 \\ \hline \end{tabular} \][/tex]
To find [tex]\(a\)[/tex], we look at the entry where [tex]\(x = -2\)[/tex] and [tex]\(f(x) = 4\)[/tex]. Since [tex]\(f\)[/tex] is even:
[tex]\[ f(-2) = f(2) \][/tex]
Hence:
[tex]\[ f(2) = 4 \][/tex]
Thus,
[tex]\[ a = 4 \][/tex]
So, the value of [tex]\(a\)[/tex] is 4.
Now let's solve for [tex]\(b\)[/tex] for the function [tex]\(g(x)\)[/tex].
We know that [tex]\(g\)[/tex] is an odd function. By definition, odd functions satisfy the following property:
[tex]\[ g(-x) = -g(x) \][/tex]
Given the table for [tex]\(g(x)\)[/tex]:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $g(x)$ \\ \hline -2 & $b$ \\ \hline 0 & 0 \\ \hline 2 & -3 \\ \hline 3 & -4 \\ \hline \end{tabular} \][/tex]
To find [tex]\(b\)[/tex], we look at the entry where [tex]\(x = 2\)[/tex] and [tex]\(g(x) = -3\)[/tex]. Since [tex]\(g\)[/tex] is odd:
[tex]\[ g(-2) = -g(2) \][/tex]
Hence:
[tex]\[ g(-2) = -(-3) = 3 \][/tex]
Thus,
[tex]\[ b = 3 \][/tex]
So, the value of [tex]\(b\)[/tex] is 3.
In conclusion:
[tex]\[ a = 4 \][/tex]
[tex]\[ b = 3 \][/tex]
We know that [tex]\(f\)[/tex] is an even function. By definition, even functions satisfy the following property:
[tex]\[ f(-x) = f(x) \][/tex]
Given the table for [tex]\(f(x)\)[/tex]:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline -2 & 4 \\ \hline 0 & 5 \\ \hline 2 & $a$ \\ \hline 3 & 7 \\ \hline \end{tabular} \][/tex]
To find [tex]\(a\)[/tex], we look at the entry where [tex]\(x = -2\)[/tex] and [tex]\(f(x) = 4\)[/tex]. Since [tex]\(f\)[/tex] is even:
[tex]\[ f(-2) = f(2) \][/tex]
Hence:
[tex]\[ f(2) = 4 \][/tex]
Thus,
[tex]\[ a = 4 \][/tex]
So, the value of [tex]\(a\)[/tex] is 4.
Now let's solve for [tex]\(b\)[/tex] for the function [tex]\(g(x)\)[/tex].
We know that [tex]\(g\)[/tex] is an odd function. By definition, odd functions satisfy the following property:
[tex]\[ g(-x) = -g(x) \][/tex]
Given the table for [tex]\(g(x)\)[/tex]:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $g(x)$ \\ \hline -2 & $b$ \\ \hline 0 & 0 \\ \hline 2 & -3 \\ \hline 3 & -4 \\ \hline \end{tabular} \][/tex]
To find [tex]\(b\)[/tex], we look at the entry where [tex]\(x = 2\)[/tex] and [tex]\(g(x) = -3\)[/tex]. Since [tex]\(g\)[/tex] is odd:
[tex]\[ g(-2) = -g(2) \][/tex]
Hence:
[tex]\[ g(-2) = -(-3) = 3 \][/tex]
Thus,
[tex]\[ b = 3 \][/tex]
So, the value of [tex]\(b\)[/tex] is 3.
In conclusion:
[tex]\[ a = 4 \][/tex]
[tex]\[ b = 3 \][/tex]
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