Q42 / 105 · JEE Main 2008 · Mathematics

Let $f: N \rightarrow Y$ be a function defined as $f(x)=4 x+3$, where $Y=\{y \in N: y=4 x+3$ for some $x \in N\}$. Show that $\mathrm{f}$ is invertible and its inverse is

  • A
    $g(y)=\frac{3 y+4}{3}$
  • B
    $g(y)=4+\frac{y+3}{4}$
  • C
    $g(y)=\frac{y+3}{4}$
  • Correct answer
    D
    $g(y)=\frac{y-3}{4}$

Solution

Function is increasing $$ x=\frac{y-3}{4}=g(y) $$

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

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