Q. Let $f:N \rightarrow Y$ be a function defined as $f(x) = 4x + 3$ where $Y = \{ y \in N:y = 4x + 3\ for\ some\ x \in N\}$. Show that $f$ is invertible and its inverse is
A) $g(y) = \frac{y - 3}{4}$
B) $g(y) = \frac{3y + 4}{3}$
C) $g(y) = 4 + \frac{y + 3}{4}$
D) $g(y) = \frac{y + 3}{4}$
Explanation
(a)
Here, $Y = \{ 7,\ 11,\ \ldots,\infty\}$
Let $y = 4x + 3 \Rightarrow \frac{y - 3}{4}$
Inverse of $f(x)$ is
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ g(y) = \frac{y - 3}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.