Chapter 5: Q. 76 (page 258)

If $f$ and $g$ are odd functions, show that the composite function $f \circ g$ is also odd.

Short Answer

Expert verified

The, $f \circ g$ is an odd function.

Step by step solution

Step 1. Given Information

Given that $f$ and $g$ are odd functions.

Step 2. Explanation

A function $f$ is said to be odd function if $f (- x) = - f (x), \forall x$ .

Since, $f$ and $g$ are odd function, So

$f (- x) = - f (x) g (- x) = - g (x)$

Now,

$f \circ g (x) = f (g (x))$

then,

$f \circ g (- x) = f (g (- x)) f \circ g (- x) = f (- g (x)) {g i s o d d f u n c t i o n .} f \circ g (- x) = - f (g (x)) {f i s o d d f u n c t i o n .} f \circ g (- x) = - f \circ g (x) \forall x$

Hence, $f \circ g$ is an odd function.

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If $f$ and $g$ are odd functions, show that the composite function $f \circ g$ is also odd.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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