If f(x+1)=x²-3x+2, then what is f(x) equal to? [NDA-I 2021]

Correct Answer is : x2−5x+6x²-5x+6x2−5x+6

If f(x+1)=x²-3x+2, then what is f(x) equal to? [NDA-I 2021]

Correct Answer is : x2−5x+6x²-5x+6x2−5x+6

Test Index

UPSC NDA I 2021 Mathematics Solved Paper

Question : 6 of 120

Marks: +1, -0

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

, then what is

f(x)

equal to?

[NDA-I 2021]

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

Validate

Solution: 👈: Video Solution

Concept:

To get the value of any function at any point with respect to some other function, we need to manipulate the given function/ point in such a way that we get the function that is needed.

Calculation:

Given,

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

\;\; =x^{2}-2x-x+2

\;\; =x(x-2)-(x-2)

\;\; =(x-2)(x-1)

\;\; =(x+1-3)(x+1-2)

\therefore f(x)=(x-3)(x-2)

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

=x^{2}-5x+6

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