Choose the correct answer from the given four options.The domain … - Vidyadip

MCQ

Choose the correct answer from the given four options.The domain of the function $\cos ^{-1}(2 x-1)$ is:

✓
$[0,1]$
B
$[-1,1]$
C
$(-1,1)$
D
$[0,\pi]$

✓

Answer

Correct option: A.

$[0,1]$

We have,$\cos ^{-1}(2 x-1)$
Now, we know that the domain of $\cos ^{-1}(x)$ is $-1\leq\text{x}\leq1$
$\therefore\ -1\leq2\text{x}-1\leq1$
Adding $1$ to all terms, we get
$\Rightarrow\ 0\leq2\text{x}\leq2$
Dividing all terms by $2,$ we get
$\Rightarrow\ 0\leq\text{x}\leq1$
$\therefore\ \text{x}\in[0,1]$

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