Question

Given f (x) =3x+7,g(x) =-x+8,h(x)=x^2+3x-1 Prove that composition of functions is associative

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Answer 1

Answer:

Since this function is continuous at x=0

Now for differentiability,

f (x) = |x| = |0| = 0 and f (0+h) = f (h) = |h|

∴limh→0−[f (0+h) − f(0)] / [h] = limh→0− |h| / h = −1 and

limh→0+[f (0+h) − f(0)] / h = limh→0+|h| / h = 1