If a + α = 1, b + β = 2 and af(x) + α f(1/x) = bx + (β)/x,x ≠ 0, then the value of the expression (f(x) + f(1/x))/(x + 1/x) is _ _ _ _ _.

Sets, Relations and Functions: JEE Main 2021 Mathematics question

JEE Main 2021 · 24 Feb, Evening shift · Q38

JEE Main 202124 Feb, Evening shiftMathematicsMediumSets, Relations and Functions168× since 2002

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 __________.

Your answerType your answer. Integers and decimals are accepted.