What is the range of f(x)=(-1)/((x+3)^2)-4 ?

The range of f(x)=(-1)/((x+3)^2)-4 is f(x)<-4

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range of f(x)=(-1)/((x+3)^2)-4

range

f (x) = \frac{- 1}{( x + 3 ) ^{2}} - 4

f (x) < - 4

Interval Notation

(- \infty, - 4)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{- 1}{( x + 3 ) ^{2}} - 4

Inverse of

\frac{- 1}{( x + 3 ) ^{2}} - 4 : - \frac{1}{x + 4} - 3, - - \frac{1}{x + 4} - 3

- \frac{1}{x + 4} - 3, - - \frac{1}{x + 4} - 3

Find the domain of each inverse function

Domain of

- \frac{1}{x + 4} - 3 : x < - 4

Domain of

- - \frac{1}{x + 4} - 3 : x < - 4

Combine the intervals

f (x) < - 4

\frac{1}{6} x^{3} - 4

y = 3 x + 3, (3, 2)

f (x) = - 5 x - 3

2 x^{2} + 5 x - 3

15 x - 3 y = 1

What is the range of f(x)=(-1)/((x+3)^2)-4 ?
The range of f(x)=(-1)/((x+3)^2)-4 is f(x)<-4