F(x) = cases x + a, & x 0 2 - x, & x < 0 cases and g(x) = cases x , & x < 0 x + b, &…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

f(x) = \begin{cases} x + a, & x \geq 0 \\ 2 - x, & x < 0 \end{cases} \text{ and } g(x) = \begin{cases} \{x\}, & x < 0 \\ \sin x + b, & x \geq 0 \end{cases}

f(g(x))

is continuous at

x = 0

, then which of the following is/are true (where

\{x\}

represents the fractional part function)? (a) If

b = 1

, then

a

can take any real value (b) If

b < -1

, then

a + b = 1

. (c) No values of

a

and

b

are possible. (d) There exist finite ordered pairs

(a, b)