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Popular >

f(x)=(2-sqrt(x^2-5))/(x+3)

Solution

f (x) = \frac{2 - x ^{2} - 5}{x + 3}

Solution

Domain : x < - 3 or - 3 < x \leq - 5 or x \geq 5

Range : - 1 < f (x) \leq - \frac{5 - 3}{2} or 1 < f (x) < \frac{3}{2} or \frac{3}{2} < f (x) \leq \frac{5 + 3}{2}

X Intercepts : (3, 0)

Asymptotes : Horizontal y = - 1, y = 1

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

+1

Interval Notation

Domain : (- \infty, - 3) \cup (- 3, - 5] \cup [5, \infty)

Range : (- 1, - \frac{5 - 3}{2}] \cup (1, \frac{3}{2}) \cup (\frac{3}{2}, \frac{5 + 3}{2}]

Solution steps

Domain of

\frac{2 - x ^{2} - 5}{x + 3} : x < - 3 or - 3 < x \leq - 5 or x \geq 5

Range of

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

Axis interception points of

\frac{2 - x ^{2} - 5}{x + 3} :

X Intercepts

: (3, 0)

Asymptotes of

\frac{2 - x ^{2} - 5}{x + 3} :

Horizontal

: y = - 1, y = 1

Extreme Points of

\frac{2 - x ^{2} - 5}{x + 3} :

Maximum

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

Maximum

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

Popular Examples

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

g(x)=(sqrt(x^4-5x^2+4))/(sqrt(x^2-5x+4))

g (x) = \frac{x ^{4} - 5 x ^{2} + 4}{x ^{2} - 5 x + 4}

f (x) = ln (x - \frac{1}{2})

f(x)=2x^3-18x+6

f (x) = 2 x^{3} - 18 x + 6

f (x) = 4 x^{3} - 3 x - 1

Frequently Asked Questions (FAQ)

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