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

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

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f(x)=sqrt((x^2+1)/(x^2+4))

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

Domain : - \infty < x < \infty

Range : \frac{1}{2} \leq f (x) < 1

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

Asymptotes : Horizontal y = 1

Extreme Points : Minimum (0, \frac{1}{2})

Interval Notation

Domain : (- \infty, \infty)

Range : [\frac{1}{2}, 1)

Solution steps

Domain of

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

Range of

\frac{x ^{2} + 1}{x ^{2} + 4} : \frac{1}{2} \leq f (x) < 1

Axis interception points of

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

Y Intercepts

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

Asymptotes of

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

Horizontal

: y = 1

Extreme Points of

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

Minimum

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

\frac{d}{d x} (1 + 9 x)

a^{8} + cos^{8} (x)

\int \frac{3 x ^{5} - 2 x ^{3} + 5 x ^{2} - 2}{x ^{3} + 1} d x

x \to 4 lim (\frac{3 x}{4} + 2)

\frac{d}{d x} ((x^{2} - 3)^{3})