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# If f : R → R be defined as f (x) = x^{2} - 3x + 2, find f (f (x))

**Solution:**

Functions are the fundamental part of calculus in mathematics.

The functions are the special types of relations.

A function in math is a rule, which gives a unique output for every input x

f : R → R be defined as

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

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

= (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

Hence, f (f (x)) = = x^{4} - 6x^{3} + 10x^{2} - 3x

NCERT Solutions for Class 12 Maths - Chapter 1 Exercise ME Question 3

## If f : R → R be defined as f (x) = x^{2} - 3x + 2, find f (f (x))

**Summary:**

For the function f : R → R be defined as f (x) = x^{2} - 3x + 2, the value of f (f (x)) = = x^{4} - 6x^{3} + 10x^{2} - 3x

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