Question

Draw the curve $\frac{2^x}{2^{\left[x\right]}}$. Where [.] denotes greatest integer function

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

We can write the given function as $f\left(x\right)=2^{x-\left[x\right]}$

We know x-[x]={x}

$\Rightarrow f\left(x\right)=2^x$

{x} varies from 0 to 1 (1 not included). We will first draw the graph of $2^x$. Then do the transformation

$2^x\to 2^x$. we will retain the part in [0,1] and it will be repeated.

[$2^{\left\{1.5\right\}}=2^{\left\{2.5\right\}}=2^{\left\{3.5\right\}}........{.2}^{\left\{0.5\right\}}=2^{0.5}$ the values get repeated]