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Popular >

f(x)=sqrt((2|x|-3)/(x^2+1))

Solution

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

Solution

Domain : x \leq - \frac{3}{2} or x \geq \frac{3}{2}

Range : 0 \leq f (x) \leq \frac{13 - 3}{2}

X Intercepts : (- \frac{3}{2}, 0), (\frac{3}{2}, 0)

Asymptotes : Horizontal y = 0

Extreme Points : Maximum \frac{- 3 - 13}{2}, \frac{13 - 3}{2}, Minimum (- \frac{3}{2}, 0), Minimum (\frac{3}{2}, 0), Maximum \frac{3 + 13}{2}, \frac{13 - 3}{2}

+1

Interval Notation

Domain : (- \infty, - \frac{3}{2}] \cup [\frac{3}{2}, \infty)

Range : 0, \frac{13 - 3}{2}

Solution steps

Domain of

\frac{2 ∣ x ∣ - 3}{x ^{2} + 1} : x \leq - \frac{3}{2} or x \geq \frac{3}{2}

Range of

\frac{2 ∣ x ∣ - 3}{x ^{2} + 1} : 0 \leq f (x) \leq \frac{13 - 3}{2}

Axis interception points of

\frac{2 ∣ x ∣ - 3}{x ^{2} + 1} :

X Intercepts

: (- \frac{3}{2}, 0), (\frac{3}{2}, 0)

Asymptotes of

\frac{2 ∣ x ∣ - 3}{x ^{2} + 1} :

Horizontal

: y = 0

Extreme Points of

\frac{2 ∣ x ∣ - 3}{x ^{2} + 1} :

Maximum

\frac{- 3 - 13}{2}, \frac{13 - 3}{2},

Minimum

(- \frac{3}{2}, 0),

Minimum

(\frac{3}{2}, 0),

Maximum

\frac{3 + 13}{2}, \frac{13 - 3}{2}

Popular Examples

F(x)=(2x^2+3x)/(x-1)

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

R(x,y,s)=((x,y))/y =2x+1

R (x, y, s) = \frac{( x , y )}{y} = 2 x + 1

f (x) = 13 - 2 x

y = \frac{5 x - 8}{2}

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

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

Frequently Asked Questions (FAQ)

What is the f(x)=sqrt((2|x|-3)/(x^2+1)) ?
The f(x)=sqrt((2|x|-3)/(x^2+1)) is