What is the range of 4sec(1/6 x)-1 ?

The range of 4sec(1/6 x)-1 is f(x) = 3

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range of 4sec(1/6 x)-1

range

4 sec (\frac{1}{6} x) - 1

f (x) \leq - 5 or f (x) \geq 3

Interval Notation

(- \infty, - 5] \cup [3, \infty)

Solution steps

The range of the basic

sec

function is

sec (\frac{1}{6} x) \leq - 1 or sec (\frac{1}{6} x) \geq 1

sec (\frac{1}{6} x) \leq - 1 or sec (\frac{1}{6} x) \geq 1

Multiply the edges of the range by:

4

4 sec (\frac{1}{6} x) \leq - 4 or 4 sec (\frac{1}{6} x) \geq 4

Add to the edges of the range:

- 1

4 sec (\frac{1}{6} x) - 1 \leq - 5 or 4 sec (\frac{1}{6} x) - 1 \geq 3

Therefore the range is

f (x) \leq - 5 or f (x) \geq 3

- 0.5 (x + 3)^{2} + 4

x + y = 6, (- 1, - 1)

7 x^{2}

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

\frac{6 x}{7 x - 1}

What is the range of 4sec(1/6 x)-1 ?
The range of 4sec(1/6 x)-1 is f(x)<=-5\lor f(x)>= 3