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Sagot :
Answer:
B. f(x) =csc(-3pi/2 x)
Step-by-step explanation:
Got it right on Edmentum.
The function [tex]f(x)=csc(-\frac{3\pi}{2x} )[/tex] is an odd function.
The correct answer is an option (B)
What is function?
- "It defines a relation between input and output values."
- "In function, for each input there is exactly one output."
What is odd function?
"A function f(x) is odd function if f(-x) = -f(x) "
For given question,
We know, cos(-x) = cos(x)
This means, cos function is an even function.
Consider, f(x) = sec (5pi/3 x)
We know,
[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex]
[tex]\Rightarrow f(x) =sec (\frac{5\pi}{3x} )\\\\\Rightarrow f(x)=\frac{1}{cos(\frac{5\pi}{3x} )}\\\\\Rightarrow f(-x)=\frac{1}{cos(-\frac{5\pi}{3x} )}\\\\\Rightarrow f(-x)=\frac{1}{cos(\frac{5\pi}{3x} )}\\\\\Rightarrow f(-x)=sec(\frac{5\pi}{3x} )\\\\\Rightarrow f(-x)=-f(x)[/tex]
This means, f(x) = sec (5pi/3 x) is an even function.
We know, sin(-x) = -sin(x)
[tex]\Rightarrow f(x)=csc(-\frac{3\pi}{2x} )\\\\\Rightarrow f(x)=\frac{1}{sin(-\frac{3\pi}{2x} )}\\\\ \Rightarrow f(-x)=\frac{1}{sin[(-\frac{3\pi}{2x} )]} \\\\\Rightarrow f(-x)=\frac{1}{-sin(-\frac{3\pi}{2x} )}\\\\\Rightarrow f(-x)=-csc(-\frac{3\pi}{2x} )}\\\\\Rightarrow f(-x)=-f(x)[/tex]
Therefore, the function [tex]f(x)=csc(-\frac{3\pi}{2x} )[/tex] is an odd function.
The correct answer is an option (B)
Learn more about odd function here:
https://brainly.com/question/14264818
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