What is the range of sqrt(|x|-1)+3 ?

The range of sqrt(|x|-1)+3 is f(x)>= 3

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range of sqrt(|x|-1)+3

range

∣ x ∣ - 1 + 3

f (x) \geq 3

Interval Notation

[3, \infty)

Solution steps

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

Domain of

∣ x ∣ - 1 + 3 : x \leq - 1 or x \geq 1

Extreme Points of

∣ x ∣ - 1 + 3 :

Minimum

(- 1, 3),

Minimum

(1, 3)

Absolute value functions are piecewise functions

Find the function intervals:

x \leq - 1, x \geq 1

Evaluate the function behavior for each interval

Find the range for the interval

- \infty < x \leq - 1 : 3 \leq f (x) < \infty

Find the range for the interval

1 \leq x < \infty : 3 \leq f (x) < \infty

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

f (x) \geq 3 or f (x) \geq 3

f (x) \geq 3

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

f (x) = 12 - 3 x

\frac{2 x ^{2} + 7 x - 15}{3 x ^{2} - 14 x + 15}

\frac{x - 5}{x}

9 - x^{3}