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Popular >

f(x)=(5x^2+1)/(x^2-2x)

Solution

f (x) = \frac{5 x ^{2} + 1}{x ^{2} - 2 x}

Solution

Domain : x < 0 or 0 < x < 2 or x > 2

Range : f (x) \leq \frac{- 21 - 1}{2} or f (x) \geq \frac{21 - 1}{2}

Intercepts : None

Asymptotes : Vertical x = 0, x = 2, Horizontal y = 5

Extreme Points : Minimum (- \frac{1 + 21}{10}, \frac{21 - 1}{2}), Maximum (\frac{21 - 1}{10}, - \frac{1 + 21}{2})

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Interval Notation

Domain : (- \infty, 0) \cup (0, 2) \cup (2, \infty)

Range : (- \infty, \frac{- 21 - 1}{2}] \cup [\frac{21 - 1}{2}, \infty)

Solution steps

Domain of

\frac{5 x ^{2} + 1}{x ^{2} - 2 x} : x < 0 or 0 < x < 2 or x > 2

Range of

\frac{5 x ^{2} + 1}{x ^{2} - 2 x} : f (x) \leq \frac{- 21 - 1}{2} or f (x) \geq \frac{21 - 1}{2}

Axis interception points of

\frac{5 x ^{2} + 1}{x ^{2} - 2 x} :

None

Asymptotes of

\frac{5 x ^{2} + 1}{x ^{2} - 2 x} :

Vertical

: x = 0, x = 2,

Horizontal

: y = 5

Extreme Points of

\frac{5 x ^{2} + 1}{x ^{2} - 2 x} :

Minimum

(- \frac{1 + 21}{10}, \frac{21 - 1}{2}),

Maximum

(\frac{21 - 1}{10}, - \frac{1 + 21}{2})

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Frequently Asked Questions (FAQ)

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