What is the range of (-3-sqrt(4x+25))/2 ?

The range of (-3-sqrt(4x+25))/2 is f(x)<=-3/2

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range of (-3-sqrt(4x+25))/2

range

\frac{- 3 - 4 x + 25}{2}

f (x) \leq - \frac{3}{2}

Interval Notation

(- \infty, - \frac{3}{2}]

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

\frac{- 3 - 4 x + 25}{2} : x \geq - \frac{25}{4}

Extreme Points of

\frac{- 3 - 4 x + 25}{2} :

Maximum

(- \frac{25}{4}, - \frac{3}{2})

Find the range for the interval

- \frac{25}{4} \leq x < \infty : - \infty < f (x) \leq - \frac{3}{2}

Combine the ranges of all domain intervals to obtain the function range

f (x) \leq - \frac{3}{2}

f (x) = - 3 x^{2} - 10 x - 8

- 20 x^{2} + 20000 x - 1800000

(0, 4), (- 5, \frac{1}{2})

2 x - 7

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

What is the range of (-3-sqrt(4x+25))/2 ?
The range of (-3-sqrt(4x+25))/2 is f(x)<=-3/2