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Popular >

f(x)=[cos(2x+1)]^3

Solution

f (x) = [cos (2 x + 1)]^{3}

Solution

Period : π

Domain : - \infty < x < \infty

Range : - 1 \leq f (x) \leq 1

X Intercepts : (- \frac{1}{2} + \frac{π}{4} + πn, 0), (- \frac{1}{2} + \frac{3 π}{4} + πn, 0), Y Intercepts : (0, cos^{3} (2 \cdot 0 + 1))

Asymptotes : None

Extreme Points : Saddle (- \frac{1}{2} + \frac{π}{4} + πn, 0), Minimum (\frac{π}{2} - \frac{1}{2} + πn, - 1), Saddle (- \frac{1}{2} + \frac{3 π}{4} + πn, 0), Maximum (\frac{- 1 + 2 π}{2} + πn, 1)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 1, 1]

Solution steps

Periodicity of

cos^{3} (2 x + 1) : π

Domain of

cos^{3} (2 x + 1) : - \infty < x < \infty

Range of

cos^{3} (2 x + 1) : - 1 \leq f (x) \leq 1

Axis interception points of

cos^{3} (2 x + 1) :

X Intercepts

: (- \frac{1}{2} + \frac{π}{4} + πn, 0), (- \frac{1}{2} + \frac{3 π}{4} + πn, 0),

Y Intercepts

: (0, cos^{3} (2 \cdot 0 + 1))

Asymptotes of

cos^{3} (2 x + 1) :

None

Extreme Points of

cos^{3} (2 x + 1) :

Saddle

(- \frac{1}{2} + \frac{π}{4} + πn, 0),

Minimum

(\frac{π}{2} - \frac{1}{2} + πn, - 1),

Saddle

(- \frac{1}{2} + \frac{3 π}{4} + πn, 0),

Maximum

(\frac{- 1 + 2 π}{2} + πn, 1)

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Frequently Asked Questions (FAQ)

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