Question

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Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Given :   $f(x)=\begin{cases}x+2 \quad if ~ x < 1\\0 \quad \quad ~~ if ~ x = 1\\x-2 \quad if ~ x > 1\end{cases}$

To Find :   Point of Discontinuity

Solution:

$f(x)=\begin{cases}x+2 \quad if ~ x < 1\\0 \quad \quad ~~ if ~ x = 1\\x-2 \quad if ~ x > 1\end{cases}$

for x  <  1

f(x) = x + 2

a linear function hence continuous

a  < 1

Lim h → 0 f(a - h)  = a - h + 2 = a + 2

f(a) = a + 2

Lim h → 0 f(a + h) = a + h + 2 = a + 2

for x > 1

f(x) = x - 2

a  linear function hence continuous

a > 1

Lim h → 0 f(a - h)  = a - h - 2 = a - 2

f(a) = a - 2

Lim h → 0 f(a + h) = a + h - 2 = a - 2

for x = 1

Lim h → 0 f(1 - h)   = x + 2  =  (1 - h) + 2 = 3 - h = 3

f(1) = 0

Lim h → 0 f(1 + h )    = x - 2  =  (1 + h) - 2 =-1 + h = -1

3 ≠ 0 ≠ - 1

Hence discontinuous at x = 1

Point of Discontinuity is x = 1

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