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

The f(x)=((x^2+2))/((x^4-3x^2+1)) is

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

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

Domain : x < - \frac{3 + 5}{2} or - \frac{3 + 5}{2} < x < - \frac{3 - 5}{2} or - \frac{3 - 5}{2} < x < \frac{3 - 5}{2} or \frac{3 - 5}{2} < x < \frac{3 + 5}{2} or x > \frac{3 + 5}{2}

Range : f (x) \leq \frac{- 2 11 - 7}{5} or f (x) > 0

Y Intercepts : (0, 2)

Asymptotes : Vertical x = - \frac{3 + 5}{2}, x = - \frac{3 - 5}{2}, x = \frac{3 - 5}{2}, x = \frac{3 + 5}{2}, Horizontal y = 0

Extreme Points : Maximum (- - 2 + 11, - \frac{2 11 + 7}{5}), Minimum (0, 2), Maximum (- 2 + 11, - \frac{2 11 + 7}{5})

Interval Notation

Domain : - \infty, - \frac{3 + 5}{2} \cup - \frac{3 + 5}{2}, - \frac{3 - 5}{2} \cup - \frac{3 - 5}{2}, \frac{3 - 5}{2} \cup \frac{3 - 5}{2}, \frac{3 + 5}{2} \cup \frac{3 + 5}{2}, \infty

Range : (- \infty, \frac{- 2 11 - 7}{5}] \cup (0, \infty)

Solution steps

Domain of

\frac{x ^{2} + 2}{x ^{4} - 3 x ^{2} + 1} : x < - \frac{3 + 5}{2} or - \frac{3 + 5}{2} < x < - \frac{3 - 5}{2} or - \frac{3 - 5}{2} < x < \frac{3 - 5}{2} or \frac{3 - 5}{2} < x < \frac{3 + 5}{2} or x > \frac{3 + 5}{2}

Range of

\frac{x ^{2} + 2}{x ^{4} - 3 x ^{2} + 1} : f (x) \leq \frac{- 2 11 - 7}{5} or f (x) > 0

Axis interception points of

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

Y Intercepts

: (0, 2)

Asymptotes of

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

Vertical

: x = - \frac{3 + 5}{2}, x = - \frac{3 - 5}{2}, x = \frac{3 - 5}{2}, x = \frac{3 + 5}{2},

Horizontal

: y = 0

Extreme Points of

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

Maximum

(- - 2 + 11, - \frac{2 11 + 7}{5}),

Minimum

(0, 2),

Maximum

(- 2 + 11, - \frac{2 11 + 7}{5})

f (x) = 2 x + 5 + 2 x^{2} + 5 x + 6

f (x) = x^{2} + 4 x + 24

f (x) = x^{4} + 21 x^{2} - 100

f (x) = sec (5 x)

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

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