Consider the function
`f(x)={{:(ax-2,"for",-2ltxlt-1),(-1,"for",-1lexle1),(a+2(x-1)^(2),"for",1lt1xlt2):}`
What is the value of a which f(x) is continuous at `x=-1` and x=1?

Options

A. `-1`
B. 1
C. 0
D. 2

Answer

A

Explanation

`f(x)={(ax-2,-2ltxlt-1),(-1,-1lexle1),(a+2(x-1)^(2),1ltxlt2):}`
if f(x) is continuous at x=-1
then, `underset(xto-1)lim(ax-2)underset(xto-1)lim(-1)`
`impliesa(\-1)-2=-1`
`impliesa=-1`
if f(x) is continuous at x=1
then, `underset(xto1)lima+2(x-1)^(2)=underset(xto1)lim-1`
`impliesa+2(1-1)^(2)=-1`
`impliesa=-1`