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UPSC NDA I and II 2020 Math Solved Paper

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Question : 69 of 120

Marks: +1, -0

What is the domain of the function

f(x) = \cos^{-1} (x - 2)

?

$[-1, 1]$
[1, 3]
[0, 5]
$[-2, 1]$

Solution:

Concept:

The inverse cosine function

\cos^{-1} y

is defined only for

y

in

[-1, 1]

.

Explanation:

Given

f(x) = \cos^{-1}(x - 2)

.

We need

x - 2

to be between

-1

and

1

(inclusive).

So we write the inequality:

-1 \le x - 2 \le 1

Add

2

to all three parts:

-1 + 2 \le x - 2 + 2 \le 1 + 2

Simplify:

1 \le x \le 3

Thus the domain is all

x

from

1

to

3

, including both endpoints.

Answer:

The domain is

[1, 3]

, which corresponds to option B.

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