Let and g(x) = f(|x|) + |f(x)|. If the number of points where g is not continuous and is not differentiable are and respectively, then is equal to ________. [2026]

Question

Let $f (x) = {\begin{matrix} e^{x - 1}, & x < 0 \\ x^{2} - 5 x + 6, & x \geq 0 \end{matrix}$ and g(x) = f(|x|) + |f(x)|. If the number of points where g is not continuous and is not differentiable are $α$ and $β$ respectively, then $α + β$ is equal to ________. [2026]

Smart Achievers · Accepted Answer

(4)

$f (x) = {\begin{matrix} e^{x - 1}, & x < 0 \\ x^{2} - 5 x + 6, & x \geq 0 \end{matrix}$ ; g(x) = f(|x|) + |f(x)|

Graph of f(x)

(f(x)) is continuous function and it is not differentiable at x = 0

Graph of |f(x)|

|f(x)| is discontinuous at x = 0

$\Rightarrow$ |f(x)| is non-differentiable at x = 0, 2, 3

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

g(x) will be discontinuous at x = 0.

So, $α = 1$

g(x) will be non-differentiable at x = 0, 2, 3.

So, $β = 3$

Hence, $α + β = 4$

Solution

Q.
Let $f (x) = {\begin{matrix} e^{x - 1}, & x < 0 \\ x^{2} - 5 x + 6, & x \geq 0 \end{matrix}$ and g(x) = f(|x|) + |f(x)|. If the number of points where g is not continuous and is not differentiable are $α$ and $β$ respectively, then $α + β$ is equal to ________. [2026]

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Solution

Q. Let f(x)={ex–1,x<0x2–5x+6,x≥0 and g(x) = f(|x|) + |f(x)|. If the number of points where g is not continuous and is not differentiable are α and β respectively, then α+β is equal to ________. [2026]

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Q.
Let $f (x) = {\begin{matrix} e^{x - 1}, & x < 0 \\ x^{2} - 5 x + 6, & x \geq 0 \end{matrix}$ and g(x) = f(|x|) + |f(x)|. If the number of points where g is not continuous and is not differentiable are $α$ and $β$ respectively, then $α + β$ is equal to ________. [2026]