Mathematics: Can anyone me? i m so stuck. i will give brainliest! 5 stars and a ! locate the points of discontinuity in the piecewise function shown below.

the answer is PERStep-by-step explanation:...

Can anyone me? i m so stuck. i will give brainliest!

Kurlyash

11.03.2022

Option A.

Step-by-step explanation:

The given piecewise function is

$f(x)=\begin{cases}-\left(x+1\right)^{2}+2 & \text{ if } x$

From the given function it is clear that function is divided at x=-1 and x=2. It means we check the discontinuity at x=-1 and x=2.

For x=-1,

f(-1)=-(-1)+2=3

LHL: $lim_{x\rightarrow -1^-}f(-1)=-\left(-1+1\right)^{2}+2=2$

Since LHL ≠ f(-1), therefore the given function is discontinuous at x=-1.

For x=2,

$f(2)=\sqrt{2-1\ }=1$

LHL: $lim_{x\rightarrow 2^-}f(2)=-(2)+2=0$

Since LHL ≠ f(2), therefore the given function is discontinuous at x=2.

Therefore, the correct option is A.

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