Question

for the following function find (a) f(3), (b) f\left(-\frac{1}{2}\
ight), (c) f(a), (d) f\left(\frac{2}{m}\
ight), and (e) any values of x such that f(x) = 1.\
\\f(x) = \

$$\begin{cases}\\frac{2x + 2}{x - 3} & \\text{if } x \ eq 3 \\\\ 2 & \\text{if } x = 3\\end{cases}$$

\\\
(c) find the value of f(a).\
\\f(a) = \

$$\begin{cases}\\frac{2a + 2}{a - 3} & \\text{if } a \ eq 3 \\\\ 2 & \\text{if } a = 3\\end{cases}$$

\\\
(d) find the value of f\left(\frac{2}{m}\
ight).\
\\f\left(\frac{2}{m}\
ight) = \

$$\begin{cases}\\frac{2m + 4}{2 - 3m} & \\text{if } m \ eq \\frac{2}{3} \\\\ \\square & \\text{if } m = \\frac{2}{3}\\end{cases}$$

\\

Explanation:

Step1: Determine condition for m=2/3

If \( m = \frac{2}{3} \), then \( \frac{2}{m} = \frac{2}{\frac{2}{3}} = 3 \).

Step2: Use function definition for x=3

The function defines \( f(3) = 2 \).

Answer:

2