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Popular >

f(x)=1-tan^2(x/2)

Solution

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

Solution

Period : 2 π

Domain : 2 πn \leq x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Range : f (x) \leq 1

X Intercepts : (\frac{π}{2} + 2 πn, 0), (\frac{3 π}{2} + 2 πn, 0), Y Intercepts : (0, 1)

Asymptotes : Vertical x = π + 2 πn

Extreme Points : Maximum (2 πn, 1)

+1

Interval Notation

Domain : [2 πn, π + 2 πn) \cup (π + 2 πn, 2 π + 2 πn)

Range : (- \infty, 1]

Solution steps

Periodicity of

1 - tan^{2} (\frac{x}{2}) : 2 π

Domain of

1 - tan^{2} (\frac{x}{2}) : 2 πn \leq x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Range of

1 - tan^{2} (\frac{x}{2}) : f (x) \leq 1

Axis interception points of

1 - tan^{2} (\frac{x}{2}) :

X Intercepts

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

Y Intercepts

: (0, 1)

Asymptotes of

1 - tan^{2} (\frac{x}{2}) :

Vertical

: x = π + 2 πn

Extreme Points of

1 - tan^{2} (\frac{x}{2}) :

Maximum

(2 πn, 1)

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f (x) = x^{3} - 12 x^{2} + 35 x - 24

Frequently Asked Questions (FAQ)

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