Home > Algebra > Domain and Range of a Function

What is the domain and range of #g(x)= 2/ (x-1)#?

Answer 1

Domain: #(-oo, 1) uu (1, +oo)#
Range: #(-oo, 0) uu (0, + oo)#

The domain of the function will be restricted by the fact that the denominator cannot be equal to zero.

#x-1!=0 implies x!=1#

The domain will thus be #RR-{1}#, or #(-oo, 1) uu (1, +oo)#.

The range of the function will be restricted by the fact that this expression cannot be equal to zero, since the numerator is a constant.

The range of the function will thus be #RR-{0}#, or #(-oo, 0) uu (0, + oo)#.

graph{2/(x-1) [-7.9, 7.9, -3.95, 3.95]}

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Isaiah Anthony

The domain of the function g(x) = 2/(x - 1) is all real numbers except x = 1, because division by zero is undefined.

The range of the function g(x) = 2/(x - 1) is all real numbers except y = 0, because the function will never equal zero since the numerator is always 2.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.