Mathematics

Problem

Consider the functions

f(x) = \tan x

and

g(x) = 2x - \frac{\tau}{2}

. a. - a Find: - i

(f \circ g)(x)

- ii

(g \circ f)(x)

b. - b Find the value of: - i

(f \circ g)\left(\frac{\tau}{3}\right)

- ii

(g \circ f)(\tau)

c. - c Write down the period and vertical asymptotes of: - i

(f \circ g)(x)

- ii

(g \circ f)(x)

d. - d Sketch the graphs of

(f \circ g)(x)

and

(g \circ f)(x)

for

-2\tau \le x \le 2\tau