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Popular >

g(x)=(x^2+x)/(2x-1)

Solution

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

Solution

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

Range : f (x) \leq - \frac{3}{2} + 1 or f (x) \geq \frac{3}{2} + 1

X Intercepts : (0, 0), (- 1, 0), Y Intercepts : (0, 0)

Asymptotes : Vertical x = \frac{1}{2}, Slant y = \frac{1}{2} x + \frac{3}{4}

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

+1

Interval Notation

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

Range : (- \infty, - \frac{3}{2} + 1] \cup [\frac{3}{2} + 1, \infty)

Solution steps

Domain of

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

Range of

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

Axis interception points of

\frac{x ^{2} + x}{2 x - 1} :

X Intercepts

: (0, 0), (- 1, 0),

Y Intercepts

: (0, 0)

Asymptotes of

\frac{x ^{2} + x}{2 x - 1} :

Vertical

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

Slant

: y = \frac{1}{2} x + \frac{3}{4}

Extreme Points of

\frac{x ^{2} + x}{2 x - 1} :

Maximum

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

Minimum

(\frac{1 + 3}{2}, \frac{3 + 2}{2})

Popular Examples

f(x)=20x^6+9x^3-20

f (x) = 20 x^{6} + 9 x^{3} - 20

y = 2 + cos (x)

f(x)=(x+4)/(x^2-8x+16)

f (x) = \frac{x + 4}{x ^{2} - 8 x + 16}

y=(3x-5)^4(7-x)^{10}

y = (3 x - 5)^{4} (7 - x)^{10}

f(x)=x^3-8x^2+16x

f (x) = x^{3} - 8 x^{2} + 16 x

Frequently Asked Questions (FAQ)

What is the g(x)=(x^2+x)/(2x-1) ?
The g(x)=(x^2+x)/(2x-1) is