Q47 / 100 · BITSAT 2024 (Memory Based Paper 1) · Mathematics

If a function $\mathbf{f}: \mathbf{R}-\{l\} \rightarrow \mathbf{R}-\{m\}$ defined by $f(x)=\frac{x+3}{x-2}$ is a bijection, then $3 l+2 m=$

  • A
    $10$
  • B
    $12$
  • Correct answer
    C
    $8$
  • D
    $14$

Solution

$f(x)=\frac{x+3}{x-2}$ $\because \quad f(x)$ is not defined for $x=2$ i.e. domain of $f(x)$ is $\mathrm{R}-\{2\}$ $\therefore l=2$ Now, $y=\frac{x+3}{x-2}$ $x y-2 y=x+3$ $x(y-1)=2 y+3$ $x=\frac{2 y+3}{y-1}$ $y$ can take any value except $y=1$ Co-domain $=\mathrm{R}-\{1\}$ $m=1$ $3 l+2 m=3(2)+2(1)=8$

Hence, the correct answer is option: 'C'.

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