What is the range of sqrt((x^2+12x-28)/(x-2)) ?

The range of sqrt((x^2+12x-28)/(x-2)) is 0 4

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range of sqrt((x^2+12x-28)/(x-2))

range

\frac{x ^{2} + 12 x - 28}{x - 2}

0 \leq f (x) < 4 or f (x) > 4

Interval Notation

[0, 4) \cup (4, \infty)

Solution steps

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

Domain of

\frac{x ^{2} + 12 x - 28}{x - 2} : - 14 \leq x < 2 or x > 2

Simplify

\frac{x ^{2} + 12 x - 28}{x - 2} : x + 14

Extreme Points of

x + 14 :

Minimum

(- 14, 0)

Find the range for the interval

- 14 \leq x < 2 : 0 \leq f (x) < 4

Find the range for the interval

2 < x < \infty : 4 < f (x) < \infty

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

0 \leq f (x) < 4 or f (x) > 4

0 \leq f (x) < 4 or f (x) > 4

f (x) = \frac{x + 2}{7 - x}

f (x) = \frac{1}{3 x ^{3} - 5}

x e^{- x}

x + 4 y = 6, (3, 2)

\frac{x ^{2} - 16}{x + 4}

What is the range of sqrt((x^2+12x-28)/(x-2)) ?
The range of sqrt((x^2+12x-28)/(x-2)) is 0<= f(x)<4\lor f(x)>4