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Popular Functions >

f(x)=((4x^2-x))/((x^2-1))

Solution

f (x) = \frac{( 4 x ^{2} - x )}{( x ^{2} - 1 )}

Solution

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

Range : f (x) \leq - \frac{15}{2} + 2 or f (x) \geq \frac{15}{2} + 2

X Intercepts : (\frac{1}{4}, 0), (0, 0), Y Intercepts : (0, 0)

Asymptotes : Vertical x = - 1, x = 1, Horizontal y = 4

Extreme Points : Maximum (4 - 15, \frac{4 - 15}{2}), Minimum (4 + 15, \frac{4 + 15}{2})

+1

Interval Notation

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

Range : (- \infty, - \frac{15}{2} + 2] \cup [\frac{15}{2} + 2, \infty)

Solution steps

Domain of

\frac{4 x ^{2} - x}{x ^{2} - 1} : x < - 1 or - 1 < x < 1 or x > 1

Range of

\frac{4 x ^{2} - x}{x ^{2} - 1} : f (x) \leq - \frac{15}{2} + 2 or f (x) \geq \frac{15}{2} + 2

Axis interception points of

\frac{4 x ^{2} - x}{x ^{2} - 1} :

X Intercepts

: (\frac{1}{4}, 0), (0, 0),

Y Intercepts

: (0, 0)

Asymptotes of

\frac{4 x ^{2} - x}{x ^{2} - 1} :

Vertical

: x = - 1, x = 1,

Horizontal

: y = 4

Extreme Points of

\frac{4 x ^{2} - x}{x ^{2} - 1} :

Maximum

(4 - 15, \frac{4 - 15}{2}),

Minimum

(4 + 15, \frac{4 + 15}{2})

Graph

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Frequently Asked Questions (FAQ)

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