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Popular >

f(x)=((1-2cos(x))^4)/2

Solution

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

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : 0 \leq f (x) \leq \frac{81}{2}

X Intercepts : (\frac{π}{3} + 2 πn, 0), (\frac{5 π}{3} + 2 πn, 0), Y Intercepts : (0, \frac{1}{2})

Asymptotes : None

Extreme Points : Maximum (2 πn, \frac{1}{2}), Minimum (\frac{π}{3} + 2 πn, 0), Maximum (π + 2 πn, \frac{81}{2}), Minimum (\frac{5 π}{3} + 2 πn, 0)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [0, \frac{81}{2}]

Solution steps

Periodicity of

\frac{( 1 - 2 cos ( x ) ) ^{4}}{2} : 2 π

Domain of

\frac{( 1 - 2 cos ( x ) ) ^{4}}{2} : - \infty < x < \infty

Range of

\frac{( 1 - 2 cos ( x ) ) ^{4}}{2} : 0 \leq f (x) \leq \frac{81}{2}

Axis interception points of

\frac{( 1 - 2 cos ( x ) ) ^{4}}{2} :

X Intercepts

: (\frac{π}{3} + 2 πn, 0), (\frac{5 π}{3} + 2 πn, 0),

Y Intercepts

: (0, \frac{1}{2})

Asymptotes of

\frac{( 1 - 2 cos ( x ) ) ^{4}}{2} :

None

Extreme Points of

\frac{( 1 - 2 cos ( x ) ) ^{4}}{2} :

Maximum

(2 πn, \frac{1}{2}),

Minimum

(\frac{π}{3} + 2 πn, 0),

Maximum

(π + 2 πn, \frac{81}{2}),

Minimum

(\frac{5 π}{3} + 2 πn, 0)

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Frequently Asked Questions (FAQ)

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