Let f: R - 3 → R - 1 be defined by f(x) = (x - 2)/(x - 3). Let g: R → R be given as g(x) = 2x - 3. Then, the sum of all the values of x for which f⁻¹(x) + g⁻¹(x) = 13/2 is equal to:

Sets, Relations and Functions: JEE Main 2021 Mathematics question

JEE Main 2021 · 18 Mar, Evening shift · Q3883

JEE Main 202118 Mar, Evening shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let f : R

-

{3}

\to

-

{1} be defined by f(x) =

{{x - 2} \over {x - 3}}

. Let g : R

\to

R be given as g(x) = 2x

-

3. Then, the sum of all the values of x for which f^

-

1(x) + g^

-

1(x) =

{{13} \over 2}

is equal to :