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Let f:ℝ→ℝ an...

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Let $f : R \to R and g : R \to R$ be respectively given by $f (x) = | x | + 1 and g (x) = x^{2} + 1. Define h : R \to R$ by
$h (x) = {\begin{matrix} max & {f (x), g (x)} & if x \leq 0, min & {f (x), g (x)} & if x > 0. \end{matrix}$
The number of points at which $h (x)$ is not differentiable is

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f : R \to R

g : R \to R

be respectively given by

f (x) = | x | + 1

g (x) = x^{2} + 1

h : R \to R

h (x) = {\begin{matrix} m a x & {f (x), g (x)} & i f & x \leq 0 m i n & {f (x), g (x)} & i f & x > 0 \end{matrix}

.
Then number of points at which

h (x)

is not differentiable is

f : R \to R

be a function such that

f (x + y) = f (x) + f (y), \forall x, y \in R .

f (x)

is differentiable at

x = 0

f : R \to R

be a function defined by

f (x) = m a x {x, x^{2}}

S

denote the set of all points in

R

f

is not differentiable. Then

f : R \to R

be a function such that

| f (x) | \leq x^{2}

x \in R

x = 0, f

f : R \to R

f (x) = \frac{x}{1 + x^{2}}, x \in R .

Then the range of

f

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