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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 : (2 πn, 0), (\frac{π}{3} + 2 πn, 0), (\frac{5 π}{3} + 2 πn, 0), Y Intercepts : (0, 0)

Asymptotes : None

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

: (2 πn, 0), (\frac{π}{3} + 2 πn, 0), (\frac{5 π}{3} + 2 πn, 0),

Y Intercepts

: (0, 0)

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, 0),

Minimum

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

Maximum

(π + 2 πn, 6),

Minimum

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

Popular Examples

f(x)=(4x^2-1)/(2x+1)

f (x) = \frac{4 x ^{2} - 1}{2 x + 1}

F (x) = 2 x + 1

y=sqrt(x)^{sqrt(x)}

y = x^{x}

y = - x^{2} - 2 x + 15

f (x) = ln (1)

Frequently Asked Questions (FAQ)

What is the f(x)=2cos^2(x)-3cos(x)+1 ?
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