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UPSC NDA II 2023 Mathematics Solved Paper

Question Numbers: 41-42

Consider the following for the next items that follow:

Let f(x) = x2 - 1 and gof(x) = x - √x + 1.

Question : 42 of 120

Marks: +1, -0

What is g(15) equal to ?

Solution:

Concept:

The function

g(x)

is defined using a square root and a fourth root of

(x+1)

, plus a constant. We evaluate it at

x=15

by direct substitution and simplification.

Explanation:

The given function is

g(x) = \sqrt{x+1} - \sqrt[4]{x+1} + 1

Substitute

x = 15

into the expression.

First compute

x+1 = 15+1 = 16

Now evaluate each term:

\sqrt{16} = 4

and

\sqrt[4]{16} = 2

(since

2^4 = 16

Thus

g(15) = 4 - 2 + 1

Simplify:

4 - 2 = 2

, then

2 + 1 = 3

Therefore

g(15) = 3

Answer:

3

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