Question

Find the domain of f(2x - 1) if the domain of f(x) is [-1,1]

• A. [-1, 1]
• B. [0, 1]
• C. [-1, 0]
• D. [1, 2]

Answer 1

The correct option is B

[0, 1]

Since the domain of f(x) is [-1,1] $\Rightarrow$ x $\in$ [-1 , 1].

Even if we write it as f(y), y $\in$ [-1,1] . In the case of f(2x - 1) , (2x - 1) $\in$ [-1,1]

- 1 $\le$ 2x - 1 $\le$ 1

$\Rightarrow$ 2x - 1 $\ge$ - 1

x $\ge$ 0

And

2x -1 $\le$ 1

x $\le$ 1

$\Rightarrow$ x $\in$ [0,1]