If f : R → R be defined as f (x) = x² - 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) = x² - 3x + 2

f (f (x)) = f (x² - 3x + 2)

= (x² - 3x + 2)² - 3(x² - 3x + 2) + 2

= (x⁴ + 9x² + 4 - 6x³ -12x + 4x² ) + (- 3x² + 9x - 6) + 2

= x⁴ - 6x³ + 10x² - 3x

Hence, f (f (x)) = = x⁴ - 6x³ + 10x² - 3x

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

If f : R → R be defined as f (x) = x² - 3x + 2, find f (f (x))

Summary:

For the function f : R → R be defined as f (x) = x² - 3x + 2, the value of f (f (x)) = = x⁴ - 6x³ + 10x² - 3x