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Popular >

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

Solution

f (x) = \frac{3 x - 5}{2 x ^{2} - x - 3}

Solution

Domain : x < - 1 or - 1 < x < \frac{3}{2} or x > \frac{3}{2}

Range : f (x) \leq \frac{9}{25} or f (x) \geq 1

X Intercepts : (\frac{5}{3}, 0), Y Intercepts : (0, \frac{5}{3})

Asymptotes : Vertical x = - 1, x = \frac{3}{2}, Horizontal y = 0

Extreme Points : Minimum (1, 1), Maximum (\frac{7}{3}, \frac{9}{25})

+1

Interval Notation

Domain : (- \infty, - 1) \cup (- 1, \frac{3}{2}) \cup (\frac{3}{2}, \infty)

Range : (- \infty, \frac{9}{25}] \cup [1, \infty)

Solution steps

Domain of

\frac{3 x - 5}{2 x ^{2} - x - 3} : x < - 1 or - 1 < x < \frac{3}{2} or x > \frac{3}{2}

Range of

\frac{3 x - 5}{2 x ^{2} - x - 3} : f (x) \leq \frac{9}{25} or f (x) \geq 1

Axis interception points of

\frac{3 x - 5}{2 x ^{2} - x - 3} :

X Intercepts

: (\frac{5}{3}, 0),

Y Intercepts

: (0, \frac{5}{3})

Asymptotes of

\frac{3 x - 5}{2 x ^{2} - x - 3} :

Vertical

: x = - 1, x = \frac{3}{2},

Horizontal

: y = 0

Extreme Points of

\frac{3 x - 5}{2 x ^{2} - x - 3} :

Minimum

(1, 1),

Maximum

(\frac{7}{3}, \frac{9}{25})

Popular Examples

f(x)=ln(2x-x^2)

f (x) = ln (2 x - x^{2})

y = - \frac{7}{2} x - 2

f(x)=sin(x)(sin(2x))

f (x) = sin (x) (sin (2 x))

f(x)=(90)/(1+271e^{-0.122x)}

f (x) = \frac{90}{1 + 271 e ^{- 0.122 x}}

y = 40 x + 500

Frequently Asked Questions (FAQ)

What is the f(x)=(3x-5)/(2x^2-x-3) ?
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