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

The range of f(x)=10-5/x is f(x) 10

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range of f(x)=10-5/x

range

f (x) = 10 - \frac{5}{x}

f (x) < 10 or f (x) > 10

Interval Notation

(- \infty, 10) \cup (10, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

10 - \frac{5}{x}

Inverse of

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

- \frac{5}{x - 10}

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < 10 or f (x) > 10

f (x) = \frac{x - 8}{7 x - 56}

x = - \frac{4}{5} y + 2

\frac{6}{x - 2}

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

y = - 2 (x + 1)^{2} + 3

What is the range of f(x)=10-5/x ?
The range of f(x)=10-5/x is f(x)<10\lor f(x)>10