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Popular Functions >

f(x)=3cos(x)-4sec(x)+3

Solution

f (x) = 3 cos (x) - 4 sec (x) + 3

Solution

Period : 2 π

Domain : 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Range : f (x) \leq 2 or f (x) \geq 4

X Intercepts : (arcsec (\frac{3 + 57}{8}) + 2 πn, 0), (2 π - arcsec (\frac{3 + 57}{8}) + 2 πn, 0), Y Intercepts : (0, 2)

Asymptotes : Vertical x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

Extreme Points : Maximum (2 πn, 2), Minimum (π + 2 πn, 4)

+1

Interval Notation

Domain : [2 πn, \frac{π}{2} + 2 πn) \cup (\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn) \cup (\frac{3 π}{2} + 2 πn, 2 π + 2 πn)

Range : (- \infty, 2] \cup [4, \infty)

Solution steps

Periodicity of

3 cos (x) - 4 sec (x) + 3 : 2 π

Domain of

3 cos (x) - 4 sec (x) + 3 : 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Range of

3 cos (x) - 4 sec (x) + 3 : f (x) \leq 2 or f (x) \geq 4

Axis interception points of

3 cos (x) - 4 sec (x) + 3 :

X Intercepts

: (arcsec (\frac{3 + 57}{8}) + 2 πn, 0), (2 π - arcsec (\frac{3 + 57}{8}) + 2 πn, 0),

Y Intercepts

: (0, 2)

Asymptotes of

3 cos (x) - 4 sec (x) + 3 :

Vertical

: x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

Extreme Points of

3 cos (x) - 4 sec (x) + 3 :

Maximum

(2 πn, 2),

Minimum

(π + 2 πn, 4)

Graph

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Frequently Asked Questions (FAQ)

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