Question

find the domain and range of f(x)=x-2/x-1

Answer 1

Answer:

The domain is all real numbers except x = 1, and the range is all real numbers except y = 1

Step-by-step explanation:

The function is given to be :

$f(x)=\frac{x-2}{x-1}$

Domain : It is defined as a set of all points for which the function is real and defined.

Now, The given function f(x) is a fraction root function and is real and defined for denominator not equal to 0. So, The domain of the given function f(x) is given by all the real numbers except zeros of denominator

⇒ x - 1 = 0

⇒ x = 1

Domain : All real numbers except x = 1

Range : It is defined as a set of all values of dependent variable for which the function is defined.

Now, To find range of the given function :

By finding the inverse of the function we can see the function f(x) can write all the real values except f(x) = 1

So, The range consists of all the real values except f(x) = 1

⇒ Range : All real numbers except f(x) = 1

Thus, The domain is all real numbers except x = 1, and the range is all real numbers except y = 1

Answer 2

Answer

x-2/x-1

domain = x-1>0

x>1

domain =(1, ∝)

range= in the denominator 0 should not come , so if we put 1 the denominator would become 0. hence range should be >1

therefore range is (1,∝)