What is the range of 1/(x^2)-4 ?

The range of 1/(x^2)-4 is f(x)>-4

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range of 1/(x^2)-4

range

\frac{1}{x ^{2}} - 4

f (x) > - 4

Interval Notation

(- 4, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{1}{x ^{2}} - 4

Inverse of

\frac{1}{x ^{2}} - 4 : \frac{1}{x + 4}, - \frac{1}{x + 4}

\frac{1}{x + 4}, - \frac{1}{x + 4}

Find the domain of each inverse function

Domain of

\frac{1}{x + 4} : x > - 4

Domain of

- \frac{1}{x + 4} : x > - 4

Combine the intervals

f (x) > - 4

cos (2000 π t)

f (x) = 5^{x} - 8

f (x) = x^{3} + 5 x^{2} - 1

f (x) = x 2 x + 1

f (x) = - x^{4} - 5 x^{3} + 6 x - 2