Home > Algebra > Domain and Range of a Function

What is the domain and range of #f(x) = 1/(2x+4)#?

Answer 1

Eva Adamson

Domain: #(-oo, -2) uu (-2, + oo)#
Range: #(-oo, 0) uu (0, + oo)#

First, note that your function can be rewritten as

#f(x) = 1/(2 * (x + 2))#

This function is defined for any value of #x in RR# except the value that would make the denominator equal to zero.

More specifically, you need to exclude from the domain of the function the value of #x# that would make

#x + 2 = 0 implies x = -2#

Therefore, the domain of the function will be #RR - {-2}#, or #(-oo, -2) uu (-2, + oo)#.

You'll see that the function can never be equal to zero because you're working with a fraction that has a constant numerator.

#f(x) !=0", "(AA)x in RR - {-2}#

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

graph{1/(2x + 4) [-3.12, 3.123, 6.243, 6.243]}

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

Answer 2

Eli Assouline

Domain: All real numbers except for x = -2.

Range: All real numbers except for y = 0.

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.