1
Question
If f : R→R is defined by f(x)=⎧⎪
⎪
⎪⎨⎪
⎪
⎪⎩x+2x2+3x+2x∈R−{−1,−2}−1x=−20x=−1then f is continuous on the set:
If f : R→R is defined by f(x)=⎧⎪
⎪
⎪⎨⎪
⎪
⎪⎩x+2x2+3x+2x∈R−{−1,−2}−1x=−20x=−1then f is continuous on the set:
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Solution
The correct option is A R−{−1}
The function f(x) can be written as,
f(x) = x+2(x+2)(x+1)
f(x) = 1x+1
Now the only point of discontinuity can be x = -1 and x = -2 where the function changes
At,x=−1
the function is not defined hence, it is discontinuous.
At x=−2,
f(x)=−1
Thus it is continuous at x = -2
So the function is discontinuous at only 1 point ie at x = -1
The function f(x) can be written as,
f(x) = x+2(x+2)(x+1)
f(x) = 1x+1
Now the only point of discontinuity can be x = -1 and x = -2 where the function changes
At,x=−1
the function is not defined hence, it is discontinuous.
At x=−2,
f(x)=−1
Thus it is continuous at x = -2
So the function is discontinuous at only 1 point ie at x = -1
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