Answer to Question #308086 in Calculus for Voice maker

Question

Question 5 [2;2]

Investigate whether the following functions are odd or even.

(a) 𝑓(𝑥) = 𝑥^

3

(b) 𝑓(𝑥) = cos 𝑥

Answer 1

A function is even if $f(-x)=f(x)$

A function is odd if $f(-x)=-f(x)$

1.

$f(x)=x³$

$f(-x)=(-x)³=-x³=-f(x)$

Hence, $f(x)=x³$ is an odd function

2.

$f(x)=cosx$

$f(-x)=cos(-x)=cosx=f(x)$

Hence, $f(x)=cosx$ is an even function