Let f:R-{3}→R-{1} be defined by fx=(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…

Question

Let f:R-{3}→R-{1} be defined by fx=(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

MARKS Content Team · Accepted Answer

Correct answer: (C) 5. fx=y=(x-2)/(x-3) ∴x=(3y-2)/(y-1) ∴f^(-1)x=(3x-2)/(x-1) & g(x)=y=2 x-3 ∴x=(y+3)/2 ∴g^(-1)x=(x+3)/2 ∵f^(-1)x+g^(-1)x=13/2 (3x-2)/(x-1)+(x+3)/2=13/2 ∴ x^2-5x+6=0 has roots x_1,x_2 ∴ sum of roots x_1+x_2=5

Let $f : R - {3} \to R - {1}$ be defined by $f (x) = \frac{x - 2}{x - 3}$ . Let $g : R \to R$ be given as $g (x) = 2 x - 3$ . Then, the sum of all the values of $x$ for which $f^{- 1} (x) + g^{- 1} (x) = \frac{13}{2}$ is equal to

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Relevant Questions

Let f:R-{3}→R-{1} be defined by fx=x-2x-3. Let g : R→R be given as g(x)=2x-3. Then, the sum of all the values of x for which f-1x+g-1x=132 is equal to

Solution

Relevant Questions

Let $f : R - {3} \to R - {1}$ be defined by $f (x) = \frac{x - 2}{x - 3}$ . Let $g : R \to R$ be given as $g (x) = 2 x - 3$ . Then, the sum of all the values of $x$ for which $f^{- 1} (x) + g^{- 1} (x) = \frac{13}{2}$ is equal to