What is the f(x)=(1+cos(6x))^{1/2} ?

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f(x)=(1+cos(6x))^{1/2}

f (x) = (1 + cos (6 x))^{\frac{1}{2}}

Domain : True for all x \in R

X Intercepts : (\frac{π}{6} + \frac{πn}{3}, 0), Y Intercepts : (0, 2^{\frac{1}{2}})

Asymptotes : None

Extreme Points : Minimum (\frac{πn}{3}, (1 + cos (2 πn))^{\frac{1}{2}})

Interval Notation

Domain : (- \infty, \infty)

Solution steps

Domain of

(1 + cos (6 x))^{\frac{1}{2}} :

True for all

x \in R

Axis interception points of

(1 + cos (6 x))^{\frac{1}{2}} :

X Intercepts

: (\frac{π}{6} + \frac{πn}{3}, 0),

Y Intercepts

: (0, 2^{\frac{1}{2}})

Asymptotes of

(1 + cos (6 x))^{\frac{1}{2}} :

None

Extreme Points of

(1 + cos (6 x))^{\frac{1}{2}} :

Minimum

(\frac{πn}{3}, (1 + cos (2 πn))^{\frac{1}{2}})

2 (sin (x))^{3} + sin (x) + tan^{5} (x)

\frac{x ^{2}}{( 1 + x ^{2} )}

\frac{y ^{2}}{4 - 1}

(1 - n) cos (x)

\frac{1}{( r - 1 )}