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MHTCET 11 Apr 2026 Shift 1 Paper

Question : 117 of 150

Marks: +1, -0

f(x)=\sqrt{x-1}+\sqrt{3-x}

is ...

Solution:

Concept:

For a square root to be defined, the expression inside it must be non-negative.

Explanation:

The function is

f(x)=\sqrt{x-1}+\sqrt{3-x}

For

\sqrt{x-1}

to be real, we need

x-1 \geq 0

So,

x \geq 1

For

\sqrt{3-x}

to be real, we need

3-x \geq 0

So,

x \leq 3

Both conditions must hold together.

Therefore,

1 \leq x \leq 3

This gives the domain as the closed interval

[1,3]

Answer:

Option C:

[1,3]

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