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Popular >

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

Solution

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

Solution

Domain : - 5 \leq x < - 2 or - 2 < x < 2 or x > 2

Range : f (x) \leq - \frac{( 19 + 5 22 ) 5 + 2 22}{168 3} or f (x) \geq 0

X Intercepts : (- 5, 0), Y Intercepts : (0, - \frac{5}{4})

Asymptotes : Vertical x = - 2, x = 2, Horizontal y = 0

Extreme Points : Minimum (- 5, 0), Maximum (- \frac{2 ( 5 - 22 )}{3}, - \frac{( 19 + 5 22 ) 5 + 2 22}{168 3})

+1

Interval Notation

Domain : [- 5, - 2) \cup (- 2, 2) \cup (2, \infty)

Range : (- \infty, - \frac{( 19 + 5 22 ) 5 + 2 22}{168 3}] \cup [0, \infty)

Solution steps

Domain of

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

Range of

\frac{x + 5}{x ^{2} - 4} : f (x) \leq - \frac{( 19 + 5 22 ) 5 + 2 22}{168 3} or f (x) \geq 0

Axis interception points of

\frac{x + 5}{x ^{2} - 4} :

X Intercepts

: (- 5, 0),

Y Intercepts

: (0, - \frac{5}{4})

Asymptotes of

\frac{x + 5}{x ^{2} - 4} :

Vertical

: x = - 2, x = 2,

Horizontal

: y = 0

Extreme Points of

\frac{x + 5}{x ^{2} - 4} :

Minimum

(- 5, 0),

Maximum

(- \frac{2 ( 5 - 22 )}{3}, - \frac{( 19 + 5 22 ) 5 + 2 22}{168 3})

Popular Examples

y=-16x^2+225x+79

y = - 16 x^{2} + 225 x + 79

y=(x-2)/((x+1)(x-3))

y = \frac{x - 2}{( x + 1 ) ( x - 3 )}

f(x)=e^x(x+xsqrt(x))

f (x) = e^{x} (x + x x)

f(x)=(3x+12)/(-x^2+16)

f (x) = \frac{3 x + 12}{- x ^{2} + 16}

f(x)=(sqrt(x-3))/(x+6)

f (x) = \frac{x - 3}{x + 6}

Frequently Asked Questions (FAQ)

What is the f(x)=(sqrt(x+5))/(x^2-4) ?
The f(x)=(sqrt(x+5))/(x^2-4) is