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Popular >

f(x)=(|x-2|)/(|x|-2)

Solution

f (x) = \frac{∣ x - 2 ∣}{∣ x ∣ - 2}

Solution

Domain : x < - 2 or - 2 < x < 2 or x > 2

Range : f (x) \leq - 1 or f (x) \geq 1

Y Intercepts : (0, - 1)

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

Extreme Points : None

+1

Interval Notation

Domain : (- \infty, - 2) \cup (- 2, 2) \cup (2, \infty)

Range : (- \infty, - 1] \cup [1, \infty)

Solution steps

Domain of

\frac{∣ x - 2 ∣}{∣ x ∣ - 2} : x < - 2 or - 2 < x < 2 or x > 2

Range of

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

Axis interception points of

\frac{∣ x - 2 ∣}{∣ x ∣ - 2} :

Y Intercepts

: (0, - 1)

Asymptotes of

\frac{∣ x - 2 ∣}{∣ x ∣ - 2} :

Vertical

: x = - 2,

Horizontal

: y = 1

Extreme Points of

\frac{∣ x - 2 ∣}{∣ x ∣ - 2} :

None

Popular Examples

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

f (x) = lo g_{3} (x^{2} - x)

f(x)=(3x)/(sqrt(x^2+2))

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

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

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

f(x)=x^4-173x^3-16x^2-7x-15

f (x) = x^{4} - 173 x^{3} - 16 x^{2} - 7 x - 15

Frequently Asked Questions (FAQ)

What is the f(x)=(|x-2|)/(|x|-2) ?
The f(x)=(|x-2|)/(|x|-2) is