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Greatest Integer Function

Let fx=15-|...

Question

Let $f (x) = 15 - | x - 10 |$ and $g (x) = f (f (x))$ then $g (x)$ is non differentiable is?

A

{5, 10, 15}

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B

{5, 10, 15, 20}

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C

{10}

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D

{5, 15}

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Solution

The correct option is A ${5, 10, 15}$
$g (x) = f (15 - | x - 10 |)$
$= 15 - | 15 - | x - 10 | - 10 | = 15 - | 5 - | x - 10 | |$
$= {\begin{matrix} 15 - | x - 5 | & x < 10 15 - | 15 - x | & 10 < x \end{matrix}$
$= ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ \begin{matrix} 10 + x & x < 5 20 - x & 5 < x < 10 x & 10 < x < 15 30 - x & 15 < x \end{matrix}$
not differentiable at $5, 10, 15$ .

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Similar questions

f (x) = 15 - | x - 10 |; x \in R

. Then the set of all values of

x

, at which the function,

g (x) = f (f (x))

is not differentiable is:

f (x) = {\begin{matrix} - 1, & - 2 \leq x < 0 x^{2} - 1, & 0 < x \leq 2 \end{matrix}

g (x) = | f (x) | + f | x |

then the number of points which

g (x)

is non differentiable, is

f (x) = | x - 2 |

g (x) = f (f (x))

\frac{d g (x)}{d x}

x > 10

f (x) = {\begin{matrix} - 1, - 2 \leq x < 0 x^{2} - 1, 0 < x \leq 2 \end{matrix}

g (x) = | f (x) | + f | x |

then the number of points at which g(x) is non differentiable, is

f (x) = | log 2 - sin x |

g (x) = f (f (x)),

x \in R

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