# What is the domain and range of `sqrt(x+5) - 4` , `1/(2x^2 - 32)` and `1/(x^2 + 1)`

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The domain of a function f(x) is the set of numbers that yield a real value for f(x). The range of a function is the set of values that f(x) can take on for values of x that lie in the domain.

The domain and range of the functions given are:

`f(x) = sqrt(x + 5) - 4` , domain `[-5, oo)` , range `[-4, oo)`

`f(x) = 1/(2x^2 - 32)` , domain is all values except for x = -4, 4 , range is `(-oo,oo)`

`f(x) = 1/(x^2 + 1)` , domain `(-oo,oo)` , Range is `(-oo,oo)`