What is t if u(v(t))=1? u(v)=cosv v(t)=t^2

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neela | High School Teacher | (Level 3) Valedictorian

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To find t if u(v(t))=1 , u(v)=cosv and v(t)=t^2.

Given u(v) = cosv and v(t) = t^2.

Therefore the composite function u(v(t)) =  cost^2.

Therefore u(v(t)) = 1 implies cost^2 = 1.

cost^2 = 1 => t^2 = 2n*pi, where n = 0,1,2,3,.....

t = +sqrt(2n*pi), or t = -sqrt(2n*pi), for n = 0,1,2,3...

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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To evaluate the value of t,we'll have to determine first the composition of the given functions u and v.

u(v(t)) is the result of composing u and v:

(uov)(t) = u(v(t))

To determine the expression of the composed function, we'll substitute v by v(t)) and we'll get:

u(v(t)) = cos v(t)

Now, we'll substitute v(t) by it's expression:

u(v(t)) = cos t^2

But, from enunciation, u(v(t))= 1, so:

cos t^2 = 1

t^2 = +/-arccos 1 + 2*k*pi

t^2 = 0 + 2*k*pi

t = +/-sqrt 2kpi

or

t = 0

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