Question

find the values of a and b that make f continuous at all points in its domain.

f(x)= {bcos(pi(x))-2 x≤ 1
3x^2-ax+b 1<x<2
2x-4a x ≥ 2

could anyone verify my answer of b= -18/5 and a =-9/5? much thanks

Answer 1

what, you can't verify your own work? Your solution gives
f(x)= {-18/5 cos(πx)-2 x≤ 1
3x^2 + 9/5 x - 18/5 1<x<2
2x + 36/5 x ≥ 2
so, at x=1, does 18/5-2 = 3 + 9/5 - 18/5 ? No ❌

we need to make sure that f(x) matches up at x=1,2
We need at x=1, -b - 2 = 3-a+b
and at x=2, 12-2a+b = 4-4a
solve those, and we have
a = -11/5 and b = -18/5

'll let you verify my answers.

Answer 2

Beep Boop answer computing. bam! you are right!

(i made a mistake doing subtractions! thank you for helping)