Let f(x) be an odd function defined on (-∞, ∞) and g(x) be an even function defined on (-∞, ∞).If f(x)-g(x)=x2+5 x+7, then g(2) is equal to

Question

Let f(x) be an odd function defined on (-∞, ∞) and g(x) be an even function defined on (-∞, ∞).If f(x)-g(x)=x2+5 x+7, then g(2) is equal to (A) -13 (B) 9 (C) 7 (D) -11

Tardigrade Admin · Accepted Answer

We have f(x)-g(x)=x2+5 x+7....(1) Replace x arrow-x in equation (1), we get f (- x )- g (- x )= x 2-5 x +7 ⇒ - f ( x )- g ( x )= x 2-5 x +7 ⇒ f ( x )+ g ( x )=- x 2+5 x -7....(2) ∴ On solving (1) and (2), we get f ( x )=5 x and g ( x )=- x 2-7 Hence g(2)=-11

Q. Let f(x) be an odd function defined on (−∞,∞) and g(x) be an even function defined on (−∞,∞).If f(x)−g(x)=x2+5x+7, then g(2) is equal to

-13

9

7

-11

We have f(x)−g(x)=x2+5x+7....(1) Replace x→−x in equation (1), we get f(−x)−g(−x)=x2−5x+7 ⇒−f(x)−g(x)=x2−5x+7 ⇒f(x)+g(x)=−x2+5x−7....(2) ∴ On solving (1) and (2), we get f(x)=5x and g(x)=−x2−7 Hence g(2)=−11

Q. Let $f (x)$ be an odd function defined on $(- \infty, \infty)$ and $g (x)$ be an even function defined on $(- \infty, \infty)$ .If $f (x) - g (x) = x^{2} + 5 x + 7$ , then $g (2)$ is equal to