Mark (√) against the correct answer in the following: If f(x) = x2

1.	Mark (√) against the correct answer in the following: If f(x) = x2 – 3x + 2 then (f o f) (x) = ? A. x4 B. x4 – 6x3 C. x4 – 6x3 + 10x2 D. None of these
Answer» Correct Answer is (D) None of these f(x) = x²– 3x + 2 ⇒f(x) = x² - 2x - x + 2 = x(x - 2) - 1(x - 2) ⇒f(x) = (x - 2)(x - 1) ⇒f(x) = (x - 2)(x - 1) ⇒f(f(x)) = ( f(x) - 2)( f(x) - 1) ⇒f(f(x)) = ((x - 2)(x - 1) - 2) ((x - 2)(x - 1) - 1) ⇒f(f(x)) = (x² – 3x + 2 - 2) (x² – 3x + 2 - 1) ⇒f(f(x)) = (x² – 3x) (x² – 3x + 1) ⇒f(f(x)) = x⁴ - 3x³ + x² - 3x³ + 9x² - 3x ⇒f(f(x)) = x⁴ - 6x³ + 10x² - 3x

Mark (√) against the correct answer in the following: If f(x) = x2 – 3x + 2 then (f o f) (x) = ? A. x4 B. x4 – 6x3 C. x4 – 6x3 + 10x2 D. None of these

Answer»

Correct Answer is (D) None of these

f(x) = x²– 3x + 2

⇒f(x) = x² - 2x - x + 2 = x(x - 2) - 1(x - 2)

⇒f(x) = (x - 2)(x - 1)

⇒f(f(x)) = ( f(x) - 2)( f(x) - 1)

⇒f(f(x)) = ((x - 2)(x - 1) - 2) ((x - 2)(x - 1) - 1)

⇒f(f(x)) = (x² – 3x + 2 - 2) (x² – 3x + 2 - 1)

⇒f(f(x)) = (x² – 3x) (x² – 3x + 1)

⇒f(f(x)) = x⁴ - 3x³ + x² - 3x³ + 9x² - 3x

⇒f(f(x)) = x⁴ - 6x³ + 10x² - 3x