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Popular Functions >

f(x)=(sqrt(4x^2+1))/(2x+3)

Solution

f (x) = \frac{4 x ^{2} + 1}{2 x + 3}

Solution

Domain : x < - \frac{3}{2} or x > - \frac{3}{2}

Range : f (x) < - 1 or f (x) \geq \frac{1}{10}

Y Intercepts : (0, \frac{1}{3})

Asymptotes : Vertical x = - \frac{3}{2}, Horizontal y = 1, y = - 1

Extreme Points : Minimum (\frac{1}{6}, \frac{1}{10})

+1

Interval Notation

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

Range : (- \infty, - 1) \cup [\frac{1}{10}, \infty)

Solution steps

Domain of

\frac{4 x ^{2} + 1}{2 x + 3} : x < - \frac{3}{2} or x > - \frac{3}{2}

Range of

\frac{4 x ^{2} + 1}{2 x + 3} : f (x) < - 1 or f (x) \geq \frac{1}{10}

Axis interception points of

\frac{4 x ^{2} + 1}{2 x + 3} :

Y Intercepts

: (0, \frac{1}{3})

Asymptotes of

\frac{4 x ^{2} + 1}{2 x + 3} :

Vertical

: x = - \frac{3}{2},

Horizontal

: y = 1, y = - 1

Extreme Points of

\frac{4 x ^{2} + 1}{2 x + 3} :

Minimum

(\frac{1}{6}, \frac{1}{10})

Graph

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Frequently Asked Questions (FAQ)

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