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Popular >

f(x)=sin^2(2x)-cos^2(2x)-1

Solution

f (x) = sin^{2} (2 x) - cos^{2} (2 x) - 1

Solution

Period : π

Domain : - \infty < x < \infty

Range : - 2 \leq f (x) \leq 0

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

Asymptotes : None

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

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 2, 0]

Solution steps

Periodicity of

sin^{2} (2 x) - cos^{2} (2 x) - 1 : π

Domain of

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

Range of

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

Axis interception points of

sin^{2} (2 x) - cos^{2} (2 x) - 1 :

X Intercepts

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

Y Intercepts

: (0, - 2)

Asymptotes of

sin^{2} (2 x) - cos^{2} (2 x) - 1 :

None

Extreme Points of

sin^{2} (2 x) - cos^{2} (2 x) - 1 :

Minimum

(πn, - 2),

Maximum

(\frac{π}{4} + πn, 0),

Minimum

(\frac{π}{2} + πn, - 2),

Maximum

(\frac{3 π}{4} + πn, 0)

Graph

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Frequently Asked Questions (FAQ)

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