QJEEM21Ma618d: JEE Main 2021 Mathematics - Class 11 JEEM21Ma618d Solution: If a + = 1, b + = 2 and , then the value of the expression is…

Question

Verified Solution • 2025–26 Session moderate

If a +

\alpha

= 1, b +

\beta

= 2 and

af(x) + \alpha f\left( {{1 \over x}} \right) = bx + {\beta \over x},x \ne 0

, then the value of the expression

{{f(x) + f\left( {{1 \over x}} \right)} \over {x + {1 \over x}}}

is __________.

Accepted Answer

af(x) + \alpha f\left( {{1 \over x}} \right) = bx + {\beta \over x}

........(i)

Replace

x

with

{1 \over x}

af\left( {{1 \over x}} \right) + af(x) = {b \over x} + \beta x

..... (ii)

(i) + (ii)

(a + \alpha )\left[ {f(x) + f\left( {{1 \over x}} \right)} \right] = \left( {x + {1 \over x}} \right)(b + \beta )

{{f(x) + f\left( {{1 \over x}} \right)} \over {x + {1 \over x}}} = {{\beta + b} \over {a + \alpha }} = {2 \over 1} = 2

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