Question

Solve for $x$: $\sqrt{x+1}-\left[x\right]=0$, where $[.]$ denotes GIF.

• A. $x=\{0,-3\}$
• B. $x=\{0,3\}$
• C. No solution
• D. $x=\left\{0\right\}$

Answer 1

The correct option is C No solution

Given: $\sqrt{x+1}-\left[x\right]=0...\left(i\right)$

Let $f:\sqrt{x+1}=y$ and $g:\left[x\right]=y$
Number of solutions of $\left(i\right)$ are same as number of points of intersection of $y=f\left(x\right)$ and $y=g\left(x\right)$.
The graphs are given by


Graphs donot intersect or cut each other.
So, there is no solution.