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Popular Functions >

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

Interval Notation

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

Range : (- \infty, \frac{1}{e}]

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})

Graph

Popular Examples

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

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

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

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

f(x)=(2x^2-x-1)/(-2x+x^2-8)

Frequently Asked Questions (FAQ)

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