What is the range of f(x)= 1/(x^2)+3 ?

The range of f(x)= 1/(x^2)+3 is f(x)>3

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range of f(x)= 1/(x^2)+3

range

f (x) = \frac{1}{x ^{2}} + 3

f (x) > 3

Interval Notation

(3, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{1}{x ^{2}} + 3

Inverse of

\frac{1}{x ^{2}} + 3 : \frac{1}{x - 3}, - \frac{1}{x - 3}

\frac{1}{x - 3}, - \frac{1}{x - 3}

Find the domain of each inverse function

Domain of

\frac{1}{x - 3} : x > 3

Domain of

- \frac{1}{x - 3} : x > 3

Combine the intervals

f (x) > 3

f (x) = 5 - x^{3}

f (x) = cos (x)

f (x) = 0.5 y - 7 = 5 x

f (x) = 6 x^{2}

f (x) = \frac{x ^{2} - 4}{x ^{3}}