Question

For what value of "a" is f(x)=
x²-1 if x≤3
2ax, if x>3

continuous over Real numbers?

Answer 1

-2 <= x <= 2 for the 1st one

Answer 2

\[\lim_{x \rightarrow 3-}x^2-1=8=\lim_{x \rightarrow 3+}2ax=\lim_{x \rightarrow 3+}6a=8, a=4/3\]

Answer 3

It's given that f(x) is continuous at 3 so limit at (3-h) is equal to (3+h) where \(h\to0\)
limit at x=3-h=> (3-h)^2-1=> 9-1=8
at x=3+h
f(3+h)=2a(3+h)=6a+2ah=6a
f(3+h)=f(3-h)
6a=8
a=4/3