What is the range of (sqrt(x-5))/(x-10) ?

The range of (sqrt(x-5))/(x-10) is -infinity <f(x)<infinity

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range of (sqrt(x-5))/(x-10)

range

\frac{x - 5}{x - 10}

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

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

Domain of

\frac{x - 5}{x - 10} : 5 \leq x < 10 or x > 10

Extreme Points of

\frac{x - 5}{x - 10} :

Maximum

(5, 0)

Find the range for the interval

5 \leq x < 10 : - \infty < f (x) \leq 0

Find the range for the interval

10 < x < \infty : 0 < f (x) < \infty

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

f (x) \leq 0 or f (x) > 0

- \infty < f (x) < \infty

x^{2} - x + 1

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

3 x^{2} - 12 x

y = 2 x + 4

y = 5 - x

What is the range of (sqrt(x-5))/(x-10) ?
The range of (sqrt(x-5))/(x-10) is -infinity <f(x)<infinity