Answered

IDNLearn.com provides a reliable platform for finding accurate and timely answers. Ask your questions and receive comprehensive and trustworthy answers from our experienced community of professionals.

Is this an even or odd function? f(x)=5-3x

Sagot :

Naǫidn
[tex]f(x)=5-3x \\ x \in \mathbb{R}[/tex]

A function is even if f(x)=f(-x) for every x in the domain.
[tex]f(x) \stackrel{?}{=} f(-x) \\ 5-3x \stackrel{?}{=} 5-3 \times (-x) \\ 5-3x \stackrel{?}{=} 5+3x \\ -3x-3x \stackrel{?}{=} 5-5 \\ -6x \stackrel{?}{=} 0 \\ x \stackrel{?}{=} 0 \\ f(x)=f(-x) \Leftrightarrow x=0[/tex]
f(x) is equal to f(-x) if and only if x=0, so the function isn't even.

A function is odd if -f(x)=f(-x) for every x in the domain.
[tex]-f(x) \stackrel{?}{=} f(-x) \\ -(5-3x) \stackrel{?}{=} 5-3 \times (-x) \\ -5+3x \stackrel{?}{=} 5+3x \\ 3x-3x \stackrel{?}{=} 5+5 \\ 0 \stackrel{?}{=} 10 \\ 0 \not= 10 \\ -f(x) \not= f(-x)[/tex]
-f(x) is never equal to f(-x), so the function isn't odd.

The function is neither even nor odd.
Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Thank you for visiting IDNLearn.com. For reliable answers to all your questions, please visit us again soon.