If $ \mathrm{f} $ is a real valued function defined by $ \mathrm{f}(\mathrm{x}+\mathrm{y})+\mathrm{f}(\mathrm{x}-\mathrm{y})=\mathrm{f}(2 \mathrm{x}) $, then the value of $ \int_{\mathrm{f}(2)}^{\mathrm{f}(-2)} \mathrm{f}(\mathrm{x}) $ is equal to

Question

If $ \mathrm{f} $ is a real valued function defined by $ \mathrm{f}(\mathrm{x}+\mathrm{y})+\mathrm{f}(\mathrm{x}-\mathrm{y})=\mathrm{f}(2 \mathrm{x}) $, then the value of $ \int_{\mathrm{f}(2)}^{\mathrm{f}(-2)} \mathrm{f}(\mathrm{x}) $ is equal to, $ 0 $, $ 1 $, $ 2 $, $ 3 $

MARKS App · Accepted Answer

f x + y + f x - y = f 2 x = f x + y + x - y Put x = 0 , y = - x f x + f - x = 0 ⇒ f x = - f x ⇒ f x is an odd function. ⇒ f 2 = - f - 2 ⇒ ∫ f 2 f - 2 f x d x = ∫ f 2 - f 2 f x d x = 0

Search any question & find its solution

Looking for more such questions to practice?