JEE PYQ: Functions Question 24
Question 24 - 2019 (08 Apr Shift 2)
Let $f(x) = a^x$ ($a > 0$) be written as $f(x) = f_1(x) + f_2(x)$, where $f_1(x)$ is an even function and $f_2(x)$ is an odd function. Then $f_1(x+y) + f_1(x-y)$ equals:
(1) $2f_1(x) f_1(y)$
(2) $2f_1(x+y) f_1(x-y)$
(3) $2f_1(x) f_2(y)$
(4) $2f_1(x) f_2(x-y)$
Type: MCQ
Show Answer
Answer: (1) $2f_1(x) f_1(y)$
Solution
$f_1(x) = \frac{a^x + a^{-x}}{2}$
$f_1(x+y) + f_1(x-y) = (a^x + a^{-x})(a^y + a^{-y})/2 = 2f_1(x) \cdot f_1(y)$
BETA
