What is the f(x)=sqrt(x+2)+1/(sqrt(3-x)) ?

The f(x)=sqrt(x+2)+1/(sqrt(3-x)) is

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f(x)=sqrt(x+2)+1/(sqrt(3-x))

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

Domain : - 2 \leq x < 3

Range : f (x) \geq \frac{1}{5}

Y Intercepts : (0, 2 + \frac{1}{3})

Asymptotes : Vertical x = 3

Extreme Points : Minimum (- 2, \frac{1}{5})

Interval Notation

Domain : [- 2, 3)

Range : [\frac{1}{5}, \infty)

Solution steps

Domain of

x + 2 + \frac{1}{3 - x} : - 2 \leq x < 3

Range of

x + 2 + \frac{1}{3 - x} : f (x) \geq \frac{1}{5}

Axis interception points of

x + 2 + \frac{1}{3 - x} :

Y Intercepts

: (0, 2 + \frac{1}{3})

Asymptotes of

x + 2 + \frac{1}{3 - x} :

Vertical

: x = 3

Extreme Points of

x + 2 + \frac{1}{3 - x} :

Minimum

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

f (x) = \frac{1 + sin ( x )}{cos ( x )}

y = 2 \cdot (\frac{1}{2})^{x}

y = x^{3} - \frac{3 x ^{2}}{2} + 3

f (x) = 5 + 4 x

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