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Popular >

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

Solution

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

Solution

Domain : x < - 1 or - 1 < x < 1 or x > 1

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

Y Intercepts : (0, - 1)

Asymptotes : Vertical x = - 1, x = 1, Horizontal y = 2

Extreme Points : Maximum (3 - 22, - \frac{2 2 - 1}{2}), Minimum (3 + 22, \frac{1 + 2 2}{2})

+1

Interval Notation

Domain : (- \infty, - 1) \cup (- 1, 1) \cup (1, \infty)

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

Solution steps

Domain of

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

Range of

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

Axis interception points of

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

Y Intercepts

: (0, - 1)

Asymptotes of

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

Vertical

: x = - 1, x = 1,

Horizontal

: y = 2

Extreme Points of

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

Maximum

(3 - 22, - \frac{2 2 - 1}{2}),

Minimum

(3 + 22, \frac{1 + 2 2}{2})

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Frequently Asked Questions (FAQ)

What is the f(x)=(2x^2-x+1)/(x^2-1) ?
The f(x)=(2x^2-x+1)/(x^2-1) is