Mathematics

Problem

A function

f: \mathbb{R} \to \mathbb{R}

is defined by

f(x)= \begin{cases} 2x+1, & x \le 0,\\ x^{2}+1, & 0 < x < 3,\\ 7, & x \ge 3. \end{cases}

Answer the following questions, showing all necessary working: (i) Find

f(-2),\;f(0),\;f(2)

and

f(3)

. (ii) Determine all real numbers

x

for which

f(x)=7

. (iii) Determine the set of all real numbers

x

for which

f(x)=5

. (iv) List the set of images of all inputs lying in the interval

[-2,2]

. a. Part 1: