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Popular >

f(x)=(2x^2-x+3)/(x^2-4x+3)

Solution

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

Solution

Domain : x < 1 or 1 < x < 3 or x > 3

Range : f (x) \leq - 32 - \frac{7}{2} or f (x) \geq 32 - \frac{7}{2}

Y Intercepts : (0, 1)

Asymptotes : Vertical x = 1, x = 3, Horizontal y = 2

Extreme Points : Minimum (- \frac{3 ( 2 2 - 1 )}{7}, \frac{6 2 - 7}{2}), Maximum (\frac{3 ( 1 + 2 2 )}{7}, - \frac{7 + 6 2}{2})

+1

Interval Notation

Domain : (- \infty, 1) \cup (1, 3) \cup (3, \infty)

Range : (- \infty, - 32 - \frac{7}{2}] \cup [32 - \frac{7}{2}, \infty)

Solution steps

Domain of

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

Range of

\frac{2 x ^{2} - x + 3}{x ^{2} - 4 x + 3} : f (x) \leq - 32 - \frac{7}{2} or f (x) \geq 32 - \frac{7}{2}

Axis interception points of

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

Y Intercepts

: (0, 1)

Asymptotes of

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

Vertical

: x = 1, x = 3,

Horizontal

: y = 2

Extreme Points of

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

Minimum

(- \frac{3 ( 2 2 - 1 )}{7}, \frac{6 2 - 7}{2}),

Maximum

(\frac{3 ( 1 + 2 2 )}{7}, - \frac{7 + 6 2}{2})

Popular Examples

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f (t) = 1 - cos (t)

y = sec (x + \frac{π}{4})

Frequently Asked Questions (FAQ)

What is the f(x)=(2x^2-x+3)/(x^2-4x+3) ?
The f(x)=(2x^2-x+3)/(x^2-4x+3) is