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

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

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

range

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

f (x) < - 4 or f (x) > - 4

Interval Notation

(- \infty, - 4) \cup (- 4, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < - 4 or f (x) > - 4

55

\frac{1}{1 - sin ( x )}

\frac{3 x + ∣ x ∣}{x}

f (x) = 8 x^{2} + 9

f (x) = \frac{9}{x + 5}

What is the range of f(x)=(4x+1)/(3-x) ?
The range of f(x)=(4x+1)/(3-x) is f(x)<-4\lor f(x)>-4