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Popular >

f(x)=(sqrt(x+5)-3)/(x^2-16)

Solution

f (x) = \frac{x + 5 - 3}{x ^{2} - 16}

Solution

Domain : - 5 \leq x < - 4 or - 4 < x < 4 or x > 4

Range : f (x) \leq \frac{9 ( - \frac{4 ( 2 + 3 )}{3} + 5 - 3 ) ( 2 3 + 1 )}{352} or 0 < f (x) < \frac{1}{48} or f (x) > \frac{1}{48}

Y Intercepts : (0, \frac{3 - 5}{16})

Asymptotes : Vertical x = - 4, Horizontal y = 0

Extreme Points : Minimum (- 5, - \frac{1}{3}), Maximum - \frac{4 ( 2 + 3 )}{3}, \frac{9 ( - \frac{4 ( 2 + 3 )}{3} + 5 - 3 ) ( 2 3 + 1 )}{352}

+1

Interval Notation

Domain : [- 5, - 4) \cup (- 4, 4) \cup (4, \infty)

Range : - \infty, \frac{9 ( - \frac{4 ( 2 + 3 )}{3} + 5 - 3 ) ( 2 3 + 1 )}{352} \cup (0, \frac{1}{48}) \cup (\frac{1}{48}, \infty)

Solution steps

Domain of

\frac{x + 5 - 3}{x ^{2} - 16} : - 5 \leq x < - 4 or - 4 < x < 4 or x > 4

Range of

\frac{x + 5 - 3}{x ^{2} - 16} : f (x) \leq \frac{9 ( - \frac{4 ( 2 + 3 )}{3} + 5 - 3 ) ( 2 3 + 1 )}{352} or 0 < f (x) < \frac{1}{48} or f (x) > \frac{1}{48}

Axis interception points of

\frac{x + 5 - 3}{x ^{2} - 16} :

Y Intercepts

: (0, \frac{3 - 5}{16})

Asymptotes of

\frac{x + 5 - 3}{x ^{2} - 16} :

Vertical

: x = - 4,

Horizontal

: y = 0

Extreme Points of

\frac{x + 5 - 3}{x ^{2} - 16} :

Minimum

(- 5, - \frac{1}{3}),

Maximum

- \frac{4 ( 2 + 3 )}{3}, \frac{9 ( - \frac{4 ( 2 + 3 )}{3} + 5 - 3 ) ( 2 3 + 1 )}{352}

Popular Examples

g(x)= x/(x^2-16)

g (x) = \frac{x}{x ^{2} - 16}

f (x) = 100 - 49 x^{2}

f(x)=5x^2+2x-13

f (x) = 5 x^{2} + 2 x - 13

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

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

f(x)=(1/2)^{x-1}+1

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

Frequently Asked Questions (FAQ)

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