Question

If f:
R-R is defined by f(x) = x2-3x+2
for
all XER, then find fof.​

Answer 1

We have , 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

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

Answer 2

Answer :

fof(x) = x⁴ - 6x³ + 10x² - 3x

Solution :

★ Given :- f : R → R , f(x) = x² - 3x + 2

★ To find :- fof(x) = ?

We have ;

f(x) = x² - 3x + 2

Thus ,

=> fof(x) = f [ f(x) ]

=> fof(x) = f (x² - 3x + 2)

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

=> fof(x) = (x²)² + (-3x)² + 2² + 2•x²•(-3x)

+ 2•(-3x)•2 + 2•2•x² - 3•x²

+ 3•3x - 3•2 + 2

=> fof(x) = x⁴ + 9x² + 4 - 6x³ - 12x + 4x²

- 3x² + 9x - 6 + 2

=> fof(x) = x⁴ - 6x³ + 10x² - 3x

Hence ,

fof(x) = x⁴ - 6x³ + 10x² - 3x