Find c such that the function f ( x ) = { x 2 − 1 x ≤ c 8 x − 17 x > c is continuous everywhere.

Question

f ( x ) = { x 2 − 1 x ≤ c

8 x − 17 x > c

c = _____

Answer 1

set x^2 -1 = 8x-17

x^2 -8x +16 = 0

(x-4)^2 = 0

x = 4

substitute into either x^2-1 or 8x-17

16-1=15 = 32-17

c=4

x^2-1 is a upward opening parabola

8x-17 is an upward sloping straight line

they meet at the point (x,c) = (4,15)

it may help to draw a rough sketch