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Popular >

f(x)=(6x^4+3x^2+1)/(3x^4+2)

Solution

f (x) = \frac{6 x ^{4} + 3 x ^{2} + 1}{3 x ^{4} + 2}

Solution

Domain : - \infty < x < \infty

Range : \frac{1}{2} \leq f (x) < 2 or 2 < f (x) \leq \frac{15 + 5}{4}

Y Intercepts : (0, \frac{1}{2})

Asymptotes : Horizontal y = 2

Extreme Points : Maximum - \frac{3 + 15}{3}, \frac{5 + 15}{4}, Minimum (0, \frac{1}{2}), Maximum \frac{3 + 15}{3}, \frac{5 + 15}{4}

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [\frac{1}{2}, 2) \cup (2, \frac{15 + 5}{4}]

Solution steps

Domain of

\frac{6 x ^{4} + 3 x ^{2} + 1}{3 x ^{4} + 2} : - \infty < x < \infty

Range of

\frac{6 x ^{4} + 3 x ^{2} + 1}{3 x ^{4} + 2} : \frac{1}{2} \leq f (x) < 2 or 2 < f (x) \leq \frac{15 + 5}{4}

Axis interception points of

\frac{6 x ^{4} + 3 x ^{2} + 1}{3 x ^{4} + 2} :

Y Intercepts

: (0, \frac{1}{2})

Asymptotes of

\frac{6 x ^{4} + 3 x ^{2} + 1}{3 x ^{4} + 2} :

Horizontal

: y = 2

Extreme Points of

\frac{6 x ^{4} + 3 x ^{2} + 1}{3 x ^{4} + 2} :

Maximum

- \frac{3 + 15}{3}, \frac{5 + 15}{4},

Minimum

(0, \frac{1}{2}),

Maximum

\frac{3 + 15}{3}, \frac{5 + 15}{4}

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Frequently Asked Questions (FAQ)

What is the f(x)=(6x^4+3x^2+1)/(3x^4+2) ?
The f(x)=(6x^4+3x^2+1)/(3x^4+2) is