Let f (x) = 15 – | x – 10 |; x ∈ R. Then the set of all values of x, at which the function, g(x) = f (f (x)) is not differentiable, is

Engineering

Mathematics

Important Points on Derivability

Question

{10}

{5, 10, 15, 20}

{10, 15}

{5, 10, 15}

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f (x) = 15 – |x – 10|, x $\in$ R

f (f (x)) = 15 – |f (x) – 10|

= 15 – |15 – |x – 10| – 10|

= 15 – |5 – |x – 10||

x = 5, 10, 15 are point of non-differentiability