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Popular >

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

Solution

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

Solution

Domain : x < - 1 or x > 1

Range : f (x) \leq \frac{1}{e}

X Intercepts : (2, 0), (- 2, 0)

Asymptotes : Vertical x = - 1, x = 1, Horizontal y = 0

Extreme Points : Maximum (- e + 1, \frac{1}{e}), Maximum (e + 1, \frac{1}{e})

+1

Solution steps

Domain of

\frac{ln ( x ^{2} - 1 )}{x ^{2} - 1} : x < - 1 or x > 1

Range of

\frac{ln ( x ^{2} - 1 )}{x ^{2} - 1} : f (x) \leq \frac{1}{e}

Axis interception points of

\frac{ln ( x ^{2} - 1 )}{x ^{2} - 1} :

X Intercepts

: (2, 0), (- 2, 0)

Asymptotes of

\frac{ln ( x ^{2} - 1 )}{x ^{2} - 1} :

Vertical

: x = - 1, x = 1,

Horizontal

: y = 0

Extreme Points of

\frac{ln ( x ^{2} - 1 )}{x ^{2} - 1} :

Maximum

(- e + 1, \frac{1}{e}),

Maximum

(e + 1, \frac{1}{e})

Popular Examples

f(x)=(5x^2+3x-2)/(x^3-4)

f (x) = \frac{5 x ^{2} + 3 x - 2}{x ^{3} - 4}

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

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

f(x)=3x^3-2x^2+4

f (x) = 3 x^{3} - 2 x^{2} + 4

f(x)=3x^3-2x^2-1

f (x) = 3 x^{3} - 2 x^{2} - 1

f(x)=(2x-6)/(x-4)+1

f (x) = \frac{2 x - 6}{x - 4} + 1

Frequently Asked Questions (FAQ)

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