Question

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

• A. $x^4-5x^3+x^2-3x$
• B. $x^4-6x^3+10x^2-3x$
• C. $x^4-3x^3+5x^2-x$
• D. None of these

Answer 1

Answer: (B)

$x^4-6x^3+10x^2-3x$

$f\left(x\right)=f(x^2-3x+2)$

$f\left(f\right(x\left)\right)=f\left(y\right)$, where $y=x^2-3x+2$

$f\left(f\right(x\left)\right)=y^2-3y+2$

$f\left(f\right(x\left)\right)=(x^2-3x+2{)}^2-3(x^2-3x+2)+2=x^4-6x^3+10x^2-3x$