For what value of the constants a and b is the function f continuous for all x

Question

f(x)= { (ax+3) if x>5

{ 8 if x=5

{ x^2 + bx + 1 if x<5

Answer 1

Since the function is continuous, so left hand limit and right and limit are equal to functional value.

Here functional value at x=5 is 8.

LHL:

ax+3=8

Sabstitute x=5, 5a+3=8, a=1

x^2+bx+1=8

Ssubstitute x=5, 5^2+5b+1=8, b=-18/5