An increasing function and a logarithmic…

Name: ______________________ Date: ____________ An increasing function and a logarithmic function (6 points)

Graph

The graph of the increasing function

f

consists of four line segments through

(0, 1)

(2, 2)

(4, 4)

(6, 5)

and

(8, 8)

, for

0 \le x \le 8

. The function

g

is defined by

g(x) = 3\ln(x - 1) - 2

for

x > 1

(A(i)) Find the value of $g(f(6))$ . Give your answer correct to three decimal places. Show the work that leads to your answer. [1 point]
(A(ii)) Find the value of $f(g(e + 1))$ . Show the work that leads to your answer. [1 point]
(B(i)) Find every value of $x$ for which $g(x) = 0.4x$ . Give each answer correct to three decimal places. [1 point]
(B(ii)) Write the behavior of $g$ as $x$ approaches $1$ from the right, using limit notation. [1 point]
(C(i)) The function $g$ is invertible. Write an expression for $g^{-1}(x)$ . [1 point]
(C(ii)) Find the exact value of $g^{-1}(f(4))$ . [1 point]

An increasing function and a logarithmic function