Nested Cos

Geometry Level 3

Find range of $f(\color{#20A900}{x})$

$\large f(\color{#20A900}{x}) = \color{#3D99F6}{cos}(\color{#0C6AC7}{\cos \color{#456461}{x}})$

None of these

[\cos 1 , 1 ]

[-\cos 1 , 1]

[0 , \cos 1 ]

[-1 , 1]

[-\cos 1 , \cos 1]

(-\infty , \infty)

\left[-\dfrac{\pi}{2} , \dfrac{\pi}{2}\right]

1 solution

Sam Maltia
Oct 7, 2015

The function would have minimum and maximum values at x=0 and x=pi/2. cos(cos(0))=cos(1), and cos(cos(pi/2))=cos(0)=1. Therefore, the function has a range of [cos(1), 1]

Incomplete solution, how did you know function is attaining its maximum value at $x = 0 , x = \dfrac{\pi}{2}$

Akhil Bansal - 5 years, 8 months ago

Because it's a cosine function. It achieves minimum/maximum values at every interval of pi/2.

Sam Maltia - 5 years, 8 months ago

Wrong..that's not cosine function, that is cos(cosx) which is different.

Akhil Bansal - 5 years, 8 months ago

@Akhil Bansal – Please elaborate.

Sam Maltia - 5 years, 8 months ago

Nested Cos

1 solution

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