Question

If \( f : R \rightarrow R\) is defined by \( f(x) = x^2-3x+2\) , find \( f (f(x)).\)

Answer 1

Answer:

f(f(x)) = x⁴ - 6x³ + 10x² - 3x

Hope this helps.

f( f(x) )

= f( x² - 3x + 2 )

= ( x² - 3x + 2 )²  -  3 ( x² - 3x + 2 )  +  2

= ( x² )² + ( 3x )² + 2² + 2(x²)(-3x) + 2(x²)(2) + 2(-3x)(2)  - 3 ( x² - 3x + 2 ) + 2

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

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

= x⁴ - 6x³ + 10x² - 3x

If you want to factorize this, it ends up as:

= x ( x - 3 ) ( x² - 3x + 1 )