f(x)= array cc 3-x, & -1 x < 0 1+ 5 x 3 , & -3 x 2 array . and g(x)= array rr -x, & -2 x 3 x, & 0 x 1 array . then range of (f o g)(x) is

Step-by-step solution

Determine the range of (f g)(x) by first finding the range of g(x) and then applying f . Interpret the definitions of f(x) and g(x) with the primary rules: g(x) = -x for x [-2, 3] and f(x) = 1 + 5x 3 for x [-3, 2] . Since g(x) = -x is decreasing on [-2, 3] , g(-2) = 2 and g(3) = -3 ; thus, the range of g(x) is [-3, 2] . Apply f(y) = 1 + 5y 3 to y [-3, 2] . As this is increasing, compute f(-3) = -4 and f(2) = 13 3 . The range of (f g)(x) is [-4, 13 3 ] . Final answer: C