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Popular >

f(x)=(cos(4x))^2

Solution

f (x) = (cos (4 x))^{2}

Solution

Period : \frac{π}{4}

Domain : - \infty < x < \infty

Range : 0 \leq f (x) \leq 1

X Intercepts : (\frac{π}{8} + \frac{πn}{4}, 0), Y Intercepts : (0, 1)

Asymptotes : None

Extreme Points : Maximum (\frac{π}{4} n, 1), Minimum (\frac{π}{8} + \frac{π}{4} n, 0)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [0, 1]

Solution steps

Periodicity of

cos^{2} (4 x) : \frac{π}{4}

Domain of

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

Range of

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

Axis interception points of

cos^{2} (4 x) :

X Intercepts

: (\frac{π}{8} + \frac{πn}{4}, 0),

Y Intercepts

: (0, 1)

Asymptotes of

cos^{2} (4 x) :

None

Extreme Points of

cos^{2} (4 x) :

Maximum

(\frac{π}{4} n, 1),

Minimum

(\frac{π}{8} + \frac{π}{4} n, 0)

Popular Examples

y = - x^{2} + 8

y = 2 cos (x + \frac{π}{4})

f (x) = x^{2} - 8 x - 8

f (x) = x^{2} - 8 x - 7

f (x) = 6 - 5 x

Frequently Asked Questions (FAQ)

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