Even and odd at the origin

Question

a. If ƒ(0) is defined and ƒ is an even function, is it necessarily true that ƒ(0) = 0? Explain.

Accepted Answer

Welcome back everyone. In this problem, considering the evil function a of x equals x to the 4th power plus c. If a of 0 is defined, which of the following statements is true about a of x? A a of 0 equals 0. B a of 0 is less than or equal to c. C a of 0 is greater than or equal to c. And the d a of 0 equals c. So if we're going to figure out which one of the statements is true, first, we need to know what a of 0 is. Now since our function a of x equals x to the 4th plus c. Then, to find a of 0, we'd substitute 0 anywhere we see x. So that tells us a of 0 equals 0 to the 4th power plus c. But 0 to the 4th power power is just 0. So that means a of 0 equals c. Looking at our answer choices, that would have been answer choice d. Thus, it is true that a of 0 equals c for the function a of x. Thanks a lot for watching everyone. I hope this video helped.

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

Even and odd at the origin

a. If ƒ(0) is defined and ƒ is an even function, is it necessarily true that ƒ(0) = 0? Explain.