If $f:R → R$ is defined by $f(x) =x

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

If $f:R → R$ is defined by $f(x) =x^2-3x+2$ then $f(f(x))$ is :

Options:

$x^4-6x^3+10x^2-2x$

$x^4-2x^3+10x^2-3x$

$x^4-6x^3+10x^2-3x$

$2x^4+6x^3-10x^2+3x$

Correct Answer:

$x^4-6x^3+10x^2-3x$

Explanation:

The correct answer is Option (3) → $x^4-6x^3+10x^2-3x$

$f(x) =x^2-3x+2$

so $f(f(x))=(x^2-3x+2)^2-3(x^2-3x+2)+2$

$=x^4+9x^2+4-6x^3-12x+4x^2-3x^2+9x-6+2$

$x^4-6x^3+10x^2-3x$