Question

If f(x) = Sin³x+x , verify that f(-x)=-f(x).

Answer 1

Answer:

f(x)= sin^3x+x

Step-by-step explanation:

put x=-x then

f(-x) = sin(-x)^3+(-x)

= -sin^3x-x

= -(sin^3x+x).

= - f(x).

Hence verified.

Answer 2

Answer:

Given:

$f(x) = sin^3 (x) + x$------------------( 1 )

To Show that f(-x) = - f(x)

If the condition f(-x) = - f(x) is satisfiied then the function is said to be an odd function.

Consider $f(x) = sin^3 (x) + x$ .

Now replace x as -x in the given function f(x).

$f(-x) = sin^3 (-x)+(-x)$,

$f(-x) = -sin^3(x)-x$,

$f(-x) = -(sin^3(x)+x)$,

From ( 1 ) we can write the above function as:

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

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