Question

If f(x)=x3-1/x3 prove that f(x)+f(1)/x=0

Answer 1

Answer:

0

Step-by-step explanation:F(X)=X3-1/X3          (GIVEN)  (EQ 1)

SAME AS , F(1/X)=1/X3-X3              (EQ 2)

BY EQUATION 1 &2

F(X)+F(1/X)=X3-1/X3+1/X3-X3

HENCE,      =0

Answer 2

Given:

f(x)=x³- 1/x³

To Find:

Prove that f(x)+f(1/x)=0.

Solution:

It is given that,

f(x)=x³- 1/x³

now find f(1/x),

for this put x = 1/x in equation f(x)=x³- 1/x³.

f(1/x) = (1/x)³ - [1/(1/x)]³

f(1/x) = 1/x³ - x³

Now,

f(x)+f(1/x)=

⇒ x³- 1/x³ + 1/x³ - x³

⇒ 0

LHS = RHS

Hence proved, f(x)+f(1/x)=0.