continuous function

**live_laugh_luv27** · August 9th 2009, 07:20 AM

Find a value for a so that the function

$f(x) = \{2x-5, x<2$
$ax^2, x\ge2$

is continuous. I came up with the answer -1/4, but not sure how, or if it is correct.
Thanks!

**Plato** · August 9th 2009, 07:50 AM

If x is near 2 but less than 2, $x \approx 2\;\& \,x < 2$ , then $2x - 5 \approx - 1$ .

If x is near 2 but greater than 2, $x \approx 2\;\& \,x > 2$ , then we must have $ax^2 \approx - 1$ . Therefore $a=\frac{-1}{4}$

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