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Question

Let f(x)={x+1:x13ax2:x>1.
Find the value of a if f is continuous at x=1.

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Solution

Given the function is f(x)={x+1:x13ax2:x>1.
Also given the function f(x) to be continuous at x=1.
Then,
limx1+f(x)=limx1f(x)=f(1)
or, 3a=2=2 [ Using the definition of the function]
or, a=32
or, a=1.

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