Question

Find domain and range of function (x) = x+4/x−2 .

Answer step by step

Answer 1

Answer:

2/x+x

Step-by-step explanation:

• x x= 4 - 2
• = x x = 2
• ans. 2/x+x

Answer 2

Given:

A function $f(x)=\frac{x+4}{x-2}$

To Find:

Find the domain and range

Solution:

To find the domain we can observe the equation and find all the values we can put in x and only terminate those which will make the equation undefined. so we can see that if we put x=2 the denominator becomes 0 which is an ill-defined value so the domain of the above equation will be

                                    $Domain=(- \infty , \infty )-[2]$

Now to find the range of the equation we need to present the above function in terms of x i.e x=f(y)

so,

$y=\frac{x+4}{x-2} \\yx-2y=x+4\\x(y-1)=2y+4\\x=\frac{2y+4}{y-1}$

so the domain of this equation becomes the range of the previous equation, using the same logic the range becomes

                                   $Range=(- \infty , \infty )-[1]$

Hence the Domain and Range of the equation are $(- \infty , \infty )-[2] and (- \infty , \infty )-[1]$.