A table, a cubic and an inverse

Name: ______________________ Date: ____________ A table, a cubic and an inverse (6 points)

Table

The table gives values of the function

f

at selected inputs. The function

g

is defined by

g(x) = 0.5x^3 - 2x + 1

for every real number

x

Values of the function f at x = -2, -1, 0, 1, 2, 3 and 4
$x$	-2	-1	0	1	2	3	4
$f(x)$	5	2	-1	3	6	2	0

(A(i)) Find the value of $f(g(2))$ , or indicate that it cannot be found from the information given. Show the work that leads to your answer. [1 point]
(A(ii)) Find every value of $x$ in the table for which $f(x) = 2$ . [1 point]
(B(i)) Find every value of $x$ for which $g(x) = 2$ . Give each answer correct to three decimal places. [1 point]
(B(ii)) Write the end behavior of $g$ as $x$ decreases without bound, using limit notation. [1 point]
(C(i)) Is $f$ invertible? Give a reason for your answer using values from the table. [1 point]
(C(ii)) Is $g$ invertible on the set of real numbers? Give a reason for your answer using specific values of $g$ . [1 point]

The question