To ensure continuity at every x, the value of the function at x = 0 and x = 2 must be equal. So, we have:
ax + 2b = 0² + 3a - b
ax + 2b = 3a - b
Since these expressions must be equal, the coefficients of x and constant terms on both sides must be equal.
Equating the coefficients of x:
a = 3
Equating the constants:
2b = -b
3b = 0
b = 0
Therefore, for the function to be continuous at every x, a = 3 and b = 0.
For what values of a and b is
F(x) = {ax+2b , xless than 0
{X²+3a-b , 0 less than x less than 2
{3x-5 , x greather than continous at every x
1 answer
1 answer