Question

The function f(x) = max {(1 - x), (1 + x), 2} is equivalent to?

• A. $f\left(x\right)=\{\begin{array}{cc}1-x& x\le -1\\ 2,& -1<x<1\\ 1+x,& x\ge 1\end{array}$
• B. $f\left(x\right)=\{\begin{array}{cc}1+x,& x\le -1\\ 2,& -1<x<1\\ 1-x,& x\ge 1\end{array}$
• C. $f\left(x\right)=\{\begin{array}{cc}1-x,& x\le -1\\ 1,& -1<x<1\\ 1+x,& x\ge 1\end{array}$
  
• D. None of these

Answer 1

The correct option is A $f\left(x\right)=\{\begin{array}{cc}1-x& x\le -1\\ 2,& -1<x<1\\ 1+x,& x\ge 1\end{array}$

We draw the graphs of y = 1 - x, y = 1 + x and y = 2

From the graph, we get
$f\left(x\right)=\{\begin{array}{ccc}1-x& if& x\le -1\\ 2& if& -1<x<1\\ 1+x& if& x\ge 1\end{array}$