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Popular >

f(x)=sec^2(x)-tan(x)-3

Solution

f (x) = sec^{2} (x) - tan (x) - 3

Solution

Period : π

Domain : πn \leq x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

Range : f (x) \geq - \frac{9}{4}

X Intercepts : (arctan (2) + πn, 0), (\frac{3 π}{4} + πn, 0), Y Intercepts : (0, - 2)

Asymptotes : Vertical x = \frac{π}{2} + πn

Extreme Points : Minimum (arctan (\frac{1}{2}) + πn, - \frac{9}{4})

+1

Interval Notation

Domain : [πn, \frac{π}{2} + πn) \cup (\frac{π}{2} + πn, π + πn)

Range : [- \frac{9}{4}, \infty)

Solution steps

Periodicity of

sec^{2} (x) - tan (x) - 3 : π

Domain of

sec^{2} (x) - tan (x) - 3 : πn \leq x < \frac{π}{2} + πn or \frac{π}{2} + πn < x < π + πn

Range of

sec^{2} (x) - tan (x) - 3 : f (x) \geq - \frac{9}{4}

Axis interception points of

sec^{2} (x) - tan (x) - 3 :

X Intercepts

: (arctan (2) + πn, 0), (\frac{3 π}{4} + πn, 0),

Y Intercepts

: (0, - 2)

Asymptotes of

sec^{2} (x) - tan (x) - 3 :

Vertical

: x = \frac{π}{2} + πn

Extreme Points of

sec^{2} (x) - tan (x) - 3 :

Minimum

(arctan (\frac{1}{2}) + πn, - \frac{9}{4})

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Frequently Asked Questions (FAQ)

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