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

solution:

 

Given: f(x) = \[x2\text{ }\text{ }3x\text{ }+\text{ }2\text{ }f\text{ }\left( f\left( x \right) \right)\text{ }=\text{ }f\left( x2\text{ }\text{ }3x\text{ }+\text{ }2 \right)\]

 

\[=\text{ }\left( x2\text{ }\text{ }3x\text{ }+\text{ }2 \right)2\text{ }\text{ }3\left( x2\text{ }\text{ }3x\text{ }+\text{ }2 \right)\text{ }+\text{ }2\]

\[=\text{ }x4\text{ }-\text{ }6×3\text{ }+\text{ }10\text{ }x2\text{ }\text{ }3x~\]