Question

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 $x \in N\}$. Its inverse is -

(1) $g(y)=4+\frac{y+3}{4}$

(2) $g(y)=\frac{y+3}{4}$

(3) $g(y)=\frac{y-3}{4}$

(4) $g(y)=\frac{3 y+3}{3}$

Answer 1

SOLUTION: $y=4 x+3 \Rightarrow x=\frac{y-3}{4} \quad \Rightarrow \quad f^{-1}(y)=g(y)=\frac{y-3}{4}$. 

Hence Option 3 is Correct.