The value of a and b is 3 and - 8 respectively.
A continuous function is one in which a continuous change in the argument results in a continuous change in the function's value. This suggests that there are no abrupt changes in value or discontinuities.
We have,
f(x) = { 1, if x ≤ 3; ax + b, if 3 < x < 5; 7, if x ≥ 5}
Since f(x) is continuous at x = 3 and x = 5,
Therefore,
At x =3,
Left-hand limit = Right hand limit
lim( x → 3-) f(x) = lim( x → 3+ ) f(x)
lim( x → 3-) (1) = lim( x → 3+ ) ( ax + b )
1 = a × 3 + b
3a + b = 1 -------------(i)
So, At x = 5
Left-hand limit = Right-hand limit
lim( x → 5-) f(x) = lim( x → 5+ ) f(x)
lim( x → 3-) (7) = lim( x → 3+ ) ( ax + b)
5(a) + b = 7 --------------(ii)
Soling the two-equation,
We get,
a = 3 and b = - 8
Learn more about continuous function here:
brainly.com/question/18102431
#SPJ9
