Question

Suppose that f is an odd function with domain R. It is know that f(4) = -5. Find f(-4).

Answer 1

Consider that $f$ is an odd function with domain $R$ and given that $f(4)=-5$

Require to find $f(-4)$

Recollect the definition of an odd function.

A function $f(x)$ is said to be an odd function if $f(-x)=-f(x)$

Using the above definition, let us find the value of $f(-4)$

Now using the above, we have

$f(-4)=-f(4)$ [ By using the definition of an odd function ]

$=-(-5)$ [ By substituting the given value: $f(4)=-5$ ]

$=5$ [ By simplification ]

Therefore, $f(-4)=5$