Question

If f(x)=x^2-1/x^2 show that f(x)=-f(1/x)​

Answer 1

Solution

Given :-

• f(x) = x² - 1/x²_________(1)

Show That :-

• f(x) = -f(1/x)

Explanation

First, keep (x = 1/x) in equ(1)

➡f(1/x) = (1/x)² - 1/(1/x)²

➡f(1/x) = 1/x² - x²

➡ - f(1/x) = x² - 1/x² _________(2)

By , equ(1) & equ(2)

➡ f(x) = - f(1/x)

Since,

• f(x) = - f(1/x)

That's proved.

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