What is the f(x)=(sqrt(x-1))/(x+1) ?

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f(x)=(sqrt(x-1))/(x+1)

f (x) = \frac{x - 1}{x + 1}

Domain : x \geq 1

Range : 0 \leq f (x) \leq \frac{1}{2 2}

X Intercepts : (1, 0)

Asymptotes : Horizontal y = 0

Extreme Points : Minimum (1, 0), Maximum (3, \frac{1}{2 2})

Interval Notation

Domain : [1, \infty)

Range : [0, \frac{1}{2 2}]

Solution steps

Domain of

\frac{x - 1}{x + 1} : x \geq 1

Range of

\frac{x - 1}{x + 1} : 0 \leq f (x) \leq \frac{1}{2 2}

Axis interception points of

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

X Intercepts

: (1, 0)

Asymptotes of

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

Horizontal

: y = 0

Extreme Points of

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

Minimum

(1, 0),

Maximum

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

\frac{d y}{d x} = \frac{( x - 4 )}{y + 6}

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

3 x^{2} - 5 x

x \to 0 lim (∣ x + 1 ∣)

\int \frac{x ^{3}}{x ^{2} + 10 x + 25} d x