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Popular Functions >

f(x)=cos(2x)

Solution

f (x) = cos (2 x)

Solution

Period : π

Domain : - \infty < x < \infty

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

X Intercepts : (\frac{π}{4} + πn, 0), (\frac{3 π}{4} + πn, 0), Y Intercepts : (0, 1)

Asymptotes : None

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

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 1, 1]

Solution steps

Periodicity of

cos (2 x) : π

Domain of

cos (2 x) : - \infty < x < \infty

Range of

cos (2 x) : - 1 \leq f (x) \leq 1

Axis interception points of

cos (2 x) :

X Intercepts

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

Y Intercepts

: (0, 1)

Asymptotes of

cos (2 x) :

None

Extreme Points of

cos (2 x) :

Maximum

(πn, 1),

Minimum

(\frac{π}{2} + πn, - 1)

Graph

Popular Examples

domain of y=ln(-x)

range of y=sqrt(x)

domain of f(x)=sqrt(x-12)

symmetry y=x^2-1

asymptotes of (2x^2)/(x^2-5x)

Frequently Asked Questions (FAQ)

What is the f(x)=cos(2x) ?
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