We are given with a function <em>y =2/(2x)</em> . So , if we cancel the <em>2</em> from both <em>numerator</em> and <em>denominator</em> we are left with <em>y = 1/x </em>. Now , here we need to find the <em>domain</em> , bur let's Recall that <em><u>Domain is the set of all values for which the given function is defined</u></em> .Now , here , if we put <em>x = 0</em> , then <em>y</em> will be <em>not defined</em> , but as for domain we <em>need only</em> the <em>set of values</em> for which the function is defined , so <em>domain</em> willn't include 0 , and for <em>all real numbers</em> except <em>0</em> , the <em>given function</em> is <em>defined</em> . So Our domain is and as this <em>interval</em> contains all <em>real numbers</em> except 0 , so domain can be further written as . Now , <em>Range</em> is the set of all <em>output values</em> of the function when we put the values of <em>domain</em> as <em>input</em> . So , now here when we put values of domain as input like let's put <em>x = -1 , -2 , -3 , -4 , 1 , 2 , 3 ,.....</em> we will get <em>y = -1 , -1/2 , -1/3 , -1/4 , 1 , 1/2 , 1/3</em><em> </em>and so on , now , the <em>input</em> will <em>give output as 0</em> , iff input is Infinite , but as input can never be infinite, so output will never comes to 0 as the <em>intervals </em>of real numbers is it's an open interval so Infinity and <em>-ve infinity</em> is not concluded in the <em>above interval</em> because whenever we think <em>a number</em> as large as much we can think , their <em>exists infinitely large numbers</em> <em>greater than</em> it , assume you're thinking <em><u>10¹⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰</u></em> as the largest number you can think , but if we add 1 in that i.e <em><u>10¹⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰ + 1</u></em> comes to be greater than it , Hence , we don't include <em>Infinity</em> and <em>-ve Infinity</em> in the interval which represents the <em>set of </em><em>all </em><em>real </em><em>numbers</em><em>. </em> So now the <em>range</em> is same as the <em>Domain</em> i.e or
<em>Hence , we concluded that : </em>
-
- Range = Domain