JEE PYQ: Functions Question 5
Question 5 - 2021 (18 Mar Shift 2)
Let $f : \mathbb{R} - {3} \to \mathbb{R} - {1}$ be defined by $f(x) = \frac{x-2}{x-3}$. Let $g : \mathbb{R} \to \mathbb{R}$ be given as $g(x) = 2x - 3$. Then, the sum of all the values of $x$ for which $f^{-1}(x) + g^{-1}(x) = \frac{13}{2}$ is equal to:
(1) 7
(2) 2
(3) 5
(4) 3
Type: MCQ
Show Answer
Answer: (3) 5
Solution
$f^{-1}(x) = \frac{3x-2}{x-1}$, $g^{-1}(x) = \frac{x+3}{2}$
$\therefore x^2 - 5x + 6 = 0$
Sum of roots $= 5$
BETA
