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allysongonzalezlove0
28.08.2019 •
Mathematics
Suppose that the function f has domain all real numbers. determine whether each function can be classified as even or odd. explain.
a) g(x)= [f(x) + f(-x)]/2
b) h(x)= [f(x) – f(-x)]/2
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Ответ:
a.Even
b.Odd
Step-by-step explanation:
We are given that function f has domain all real numbers .
We have to find that given function is even or odd
a.![g(x)=\frac{f(x)+f(-x)}{2}](/tpl/images/0205/9838/663be.png)
We know that if function is even then f(x)=f(-x) and if function is odd then![f(x)\neq f(-x)](/tpl/images/0205/9838/8ab98.png)
Replace x by -x then we get
Therefore, function is even .
b.![h(x)=\frac{f(x)-f(-x)}{2}](/tpl/images/0205/9838/1e7d0.png)
Replace x by -x
Then we get![h(x)=\frac{f(-x)-f(x)}{2}=-\frac{f(x)-f(-x)}{2}](/tpl/images/0205/9838/4b51e.png)
Hence, function is odd.
Ответ:
Tbh man I honestly don’t know