Question

If f:R → R is defined by f(x) = x2 – 3x + 2, find f(f(x)).​

Answer 1

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

Answer 2

Answer:

x^4  -6x^3  +10x^2  -12x

Step-by-step explanation:

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

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

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

f(f(x)) = (x^2 -3x +2)((x^2 -3x -1) +2

f(f(x)) = x^4  -3x^3  -x^2  -3x^3 + 9x^2  -6x  +2x^2  -6x  -2  +2

f(f(x)) = x^4  -6x^3  +10x^2  -12x