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Popular >

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

Solution

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

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - \frac{1}{4} \leq f (x) \leq 2

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

Asymptotes : None

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

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{1}{4}, 2]

Solution steps

Periodicity of

cos (x) + cos^{2} (x) : 2 π

Domain of

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

Range of

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

Axis interception points of

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

X Intercepts

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

Y Intercepts

: (0, 2)

Asymptotes of

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

None

Extreme Points of

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

Maximum

(2 πn, 2),

Minimum

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

Maximum

(π + 2 πn, 0),

Minimum

(\frac{4 π}{3} + 2 πn, - \frac{1}{4})

Popular Examples

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f (x) = 2 x^{2} + 8 x + 4

f(x)=4^x+2^{x+1}+3

f (x) = 4^{x} + 2^{x + 1} + 3

f(x)=-x^2+2x+15

f (x) = - x^{2} + 2 x + 15

y = (x + 3) (x - 3)

Frequently Asked Questions (FAQ)

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