Test Index

UPSC NDA I 2021 Mathematics Solved Paper

© examsnet.com

Question : 6 of 120

Marks: +1, -0

If

f(x + 1) = x^{2} - 3x + 2

f(x)

equal to?

$x^{2} - 5x + 4$
$x^{2} - 5x + 6$
$x^{2} + 3x + 3$
$x^{2} - 3x + 1$

Solution:

Concept:

To find

f(x)

from

f(x+1)

, we can replace

x

with

(x-1)

in the given expression.

Explanation:

Given

f(x+1) = x^{2} - 3x + 2

.

Let

x

be replaced by

(x-1)

in the input of

f

.

Then

f((x-1) + 1) = f(x) = (x-1)^{2} - 3(x-1) + 2

.

Simplify step by step:

(x-1)^{2} = x^{2} - 2x + 1

.

-3(x-1) = -3x + 3

.

So

f(x) = (x^{2} - 2x + 1) + (-3x + 3) + 2

.

Combine like terms:

x^{2} - 2x - 3x + 1 + 3 + 2 = x^{2} - 5x + 6

.

Thus

f(x) = x^{2} - 5x + 6

.

Answer:

f(x) = x^{2} - 5x + 6

(Option B).

© examsnet.com

Go to Question:

Prev Question

Next Question