Let ` 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, isA. `{5, 10, 15, 20}`B. ` {5, 10, 15}`C. ` { 10}`D. `{10, 15}`

Let ` f(x) = 15 -|x-10|, x in R`. Then, the set of all values of x, at

1.	Let ` 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, isA. `{5, 10, 15, 20}`B. ` {5, 10, 15}`C. ` { 10}`D. `{10, 15}`
Answer» Correct Answer - B Given function is `f(x) = 15 - \|x-10\|, x in R and g(x) = f(f(x))` `= f(15-\|x-10\|)` ` = 15-\|15-\|x-10\|-10\|` ` = 15-\|5-\|x - 10\|\|` `{{:(15-\|5-(x-10)\|" , "x ge 10),(15-\|5+(x-10)\|" , " x lt 10):}` ` ={{:(15-\|15-x\|" , " x ge 10),(15-\|x-5\|" , " x lt 10):}` `={{:(15+(x-5)= 10 +x" , "x lt 5),(15-(x-5)=20-x" , "5le x lt 10),( 15+(x-15) = x" , " 10 le x lt 15),(15-(x-15) = 30-x", " x ge 15):}` From the above definition it is clear that g(x) is not differentiable at x = 5, 10, 15.