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Popular >

f(x)=2cos^2(x)+3cos(x)+1

Solution

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

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - \frac{1}{8} \leq f (x) \leq 6

X Intercepts : (\frac{2 π}{3} + 2 πn, 0), (\frac{4 π}{3} + 2 πn, 0), (π + 2 πn, 0), Y Intercepts : (0, 6)

Asymptotes : None

Extreme Points : Maximum (2 πn, 6), Minimum (arccos (- \frac{3}{4}) + 2 πn, - \frac{1}{8}), Maximum (π + 2 πn, 0), Minimum (- arccos (- \frac{3}{4}) + 2 π + 2 πn, - \frac{1}{8})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{1}{8}, 6]

Solution steps

Periodicity of

2 cos^{2} (x) + 3 cos (x) + 1 : 2 π

Domain of

2 cos^{2} (x) + 3 cos (x) + 1 : - \infty < x < \infty

Range of

2 cos^{2} (x) + 3 cos (x) + 1 : - \frac{1}{8} \leq f (x) \leq 6

Axis interception points of

2 cos^{2} (x) + 3 cos (x) + 1 :

X Intercepts

: (\frac{2 π}{3} + 2 πn, 0), (\frac{4 π}{3} + 2 πn, 0), (π + 2 πn, 0),

Y Intercepts

: (0, 6)

Asymptotes of

2 cos^{2} (x) + 3 cos (x) + 1 :

None

Extreme Points of

2 cos^{2} (x) + 3 cos (x) + 1 :

Maximum

(2 πn, 6),

Minimum

(arccos (- \frac{3}{4}) + 2 πn, - \frac{1}{8}),

Maximum

(π + 2 πn, 0),

Minimum

(- arccos (- \frac{3}{4}) + 2 π + 2 πn, - \frac{1}{8})

Popular Examples

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y = \frac{2}{x - 1}

f(x)=1+\sqrt[3]{x}

y = - 2 (x + 4)^{2} - 1

y = - 2 (x + 4)^{2} + 3

Frequently Asked Questions (FAQ)

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