Let f : [ 0 , 4 ] [ 0 , ] be defined by f ( x ) = cos - 1 ( cos x ) . The number of points x [ 0 , 4 ] satisfying the equation g ( x ) = 10 - x 10 is [2014]

Question

Let $f : [0, 4 π] \to [0, π]$ be defined by $f (x) = \cos^{- 1} (\cos x) .$ The number of points $x \in [0, 4 π]$ satisfying the equation $g (x) = \frac{10 - x}{10}$ is [2014]

Smart Achievers · Accepted Answer

(3)

$Given: f : [0, 4 π] \to [0, π] defined by$

$f (x) = \cos^{- 1} (\cos x)$

and $g (x) = \frac{10 - x}{10} = 1 - \frac{x}{10}$

The graph of $y = f (x)$ and $y = g (x)$ are as follows.

Solution

Q.
Let $f : [0, 4 π] \to [0, π]$ be defined by $f (x) = \cos^{- 1} (\cos x) .$ The number of points $x \in [0, 4 π]$ satisfying the equation $g (x) = \frac{10 - x}{10}$ is [2014]

Ans.
(3)

$Given: f : [0, 4 π] \to [0, π] defined by$

$f (x) = \cos^{- 1} (\cos x)$

and $g (x) = \frac{10 - x}{10} = 1 - \frac{x}{10}$

The graph of $y = f (x)$ and $y = g (x)$ are as follows.

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Solution

Q. Let f:[0,4π]→[0,π] be defined by f(x)=cos-1(cosx). The number of points x∈[0,4π] satisfying the equation g(x)=10-x10 is [2014]

Ans. (3) Given: f:[0,4π]→[0,π] defined by f(x)=cos-1(cosx) and g(x)=10-x10=1-x10 The graph of y=f(x) and y=g(x) are as follows.

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Q.
Let $f : [0, 4 π] \to [0, π]$ be defined by $f (x) = \cos^{- 1} (\cos x) .$ The number of points $x \in [0, 4 π]$ satisfying the equation $g (x) = \frac{10 - x}{10}$ is [2014]

Ans.
(3)

$Given: f : [0, 4 π] \to [0, π] defined by$

$f (x) = \cos^{- 1} (\cos x)$

and $g (x) = \frac{10 - x}{10} = 1 - \frac{x}{10}$

The graph of $y = f (x)$ and $y = g (x)$ are as follows.