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

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

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range of (-4)/(x^2)+1

range

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

f (x) < 1

Interval Notation

(- \infty, 1)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

- \frac{4}{x - 1} : x < 1

Domain of

- - \frac{4}{x - 1} : x < 1

Combine the intervals

f (x) < 1

f (x) = \frac{1 + x}{7 - x}

f (x) = 3 x^{4} - 18 x^{2}

f (x) = \frac{1}{4} tan (6 x)

(x - 1)^{2} + 6

f (x) = 7 x + \frac{5}{x + 2}