Question

1. Find the constant a such that the function f is continuous on the entire real number line, where 3x2, x ≥ 1 ax−4, x<1 Hint: the curve from the right hand side and the curve from the left hand of x = 1 must meet at point (1,f(1)).

Answer 1

Answer:

  a = 7

Step-by-step explanation:

The function given is defined at x=1 as ...

  f(1) = 3·1² = 3

In order to make the limit from the left be 3, we must have ...

  ax -4 = 3 . . . . for x=1

  1a = 7 . . . . . . .add 4

The value of the constant "a" is 7.