Question

Assertion :$f:R\to R$ defined by $f\left(x\right)=7x-\left[7x\right]$ where $[\cdot ]$ denotes greatest integer less than equal to $x$ and $x\in R$, $f$ is not one-one function. Reason: Periodic functions are always many one.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Given $f\left(x\right)=7x-\left[7x\right]=\left\{7x\right\}$

We know $\left\{x\right\}$ is a periodic function with a period $1$.

$\Rightarrow$ $f\left(x\right)$is periodic with period $\frac{1}{7}$

$\Rightarrow$ Periodic functions are many one functions.
$\Rightarrow$ Reason is true and many one functions can not be one-one function so Assertion is true