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Popular Functions >

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

Solution

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

Solution

Domain : x \leq - 2^{\frac{1}{2}} or x \geq 2^{\frac{1}{2}}

Range : - 3 \cdot 2^{\frac{1}{2}} \leq f (x) < 3

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

Asymptotes : Horizontal y = - 3, y = 3

Extreme Points : Minimum (- 2, 0), Maximum (2, 0), Minimum (2, - 3 \cdot 2^{\frac{1}{2}})

+1

Interval Notation

Domain : (- \infty, - 2^{\frac{1}{2}}] \cup [2^{\frac{1}{2}}, \infty)

Range : [- 3 2^{\frac{1}{2}}, 3)

Solution steps

Domain of

\frac{3 ( x ^{2} - 2 ) ^{\frac{1}{2}}}{1 - x} : x \leq - 2^{\frac{1}{2}} or x \geq 2^{\frac{1}{2}}

Range of

\frac{3 ( x ^{2} - 2 ) ^{\frac{1}{2}}}{1 - x} : - 3 \cdot 2^{\frac{1}{2}} \leq f (x) < 3

Axis interception points of

\frac{3 ( x ^{2} - 2 ) ^{\frac{1}{2}}}{1 - x} :

X Intercepts

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

Asymptotes of

\frac{3 ( x ^{2} - 2 ) ^{\frac{1}{2}}}{1 - x} :

Horizontal

: y = - 3, y = 3

Extreme Points of

\frac{3 ( x ^{2} - 2 ) ^{\frac{1}{2}}}{1 - x} :

Minimum

(- 2, 0),

Maximum

(2, 0),

Minimum

(2, - 3 \cdot 2^{\frac{1}{2}})

Graph

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Frequently Asked Questions (FAQ)

What is the f(x)=(3(x^2-2)^{1/2})/(1-x) ?
The f(x)=(3(x^2-2)^{1/2})/(1-x) is