What is the range of sqrt(x^2-2)-4 ?

The range of sqrt(x^2-2)-4 is f(x)>=-4

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range of sqrt(x^2-2)-4

range

x^{2} - 2 - 4

f (x) \geq - 4

Solution steps

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

Domain of

x^{2} - 2 - 4 : x \leq - 2 or x \geq 2

Extreme Points of

x^{2} - 2 - 4 :

Minimum

(- 2, - 4),

Minimum

(2, - 4)

Find the range for the interval

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

Find the range for the interval

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

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

f (x) \geq - 4 or f (x) \geq - 4

f (x) \geq - 4

(- 1, 0), (0, 1)

y = - x + 2

x + y = 3

f (x) = (x - 4) (\frac{x}{2} + 1)^{3}

\frac{x - 4}{2 x - 12}