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

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

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

range

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

f (x) > 1

Interval Notation

(1, \infty)

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

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

Simplify

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

Extreme Points of

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

None

Find the range for the interval

4 < x < \infty : 1 < f (x) < \infty

Combine the ranges of all domain intervals to obtain the function range

f (x) > 1

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

y = x + 3

y = - \frac{2}{3} + 8

f (x) = \frac{5}{x + 1}

f (x) = 5 - \frac{3}{4} x

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