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Popular >

f(x)=(x^3-4x)/(-4x^2+12x)

Solution

f (x) = \frac{x ^{3} - 4 x}{- 4 x ^{2} + 12 x}

Solution

Domain : x < 0 or 0 < x < 3 or x > 3

Range : f (x) \leq - \frac{5 + 3}{2} or f (x) \geq \frac{5 - 3 5}{2 5}

X Intercepts : (2, 0), (- 2, 0)

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

Extreme Points : Minimum (3 - 5, \frac{5 - 3}{2}), Maximum (3 + 5, - \frac{3 + 5}{2})

+1

Interval Notation

Domain : (- \infty, 0) \cup (0, 3) \cup (3, \infty)

Range : (- \infty, - \frac{5 + 3}{2}] \cup [\frac{5 - 3 5}{2 5}, \infty)

Solution steps

Domain of

\frac{x ^{3} - 4 x}{- 4 x ^{2} + 12 x} : x < 0 or 0 < x < 3 or x > 3

Range of

\frac{x ^{3} - 4 x}{- 4 x ^{2} + 12 x} : f (x) \leq - \frac{5 + 3}{2} or f (x) \geq \frac{5 - 3 5}{2 5}

Axis interception points of

\frac{x ^{3} - 4 x}{- 4 x ^{2} + 12 x} :

X Intercepts

: (2, 0), (- 2, 0)

Asymptotes of

\frac{x ^{3} - 4 x}{- 4 x ^{2} + 12 x} :

Vertical

: x = 3,

Slant

: y = - \frac{1}{4} x - \frac{3}{4}

Extreme Points of

\frac{x ^{3} - 4 x}{- 4 x ^{2} + 12 x} :

Minimum

(3 - 5, \frac{5 - 3}{2}),

Maximum

(3 + 5, - \frac{3 + 5}{2})

Popular Examples

f(x)=x^5-3x^4-5x^3+5x^2-6x+8

f (x) = x^{5} - 3 x^{4} - 5 x^{3} + 5 x^{2} - 6 x + 8

f(t)=(t^2-t+1)/(t^2+1)

f (t) = \frac{t ^{2} - t + 1}{t ^{2} + 1}

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

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

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

y = \frac{1 + x ^{2}}{1 - x ^{2}}

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

Frequently Asked Questions (FAQ)

What is the f(x)=(x^3-4x)/(-4x^2+12x) ?
The f(x)=(x^3-4x)/(-4x^2+12x) is