(2) f(x)=x^2-2 x [ f(x)=x+1 (f circ f)(x)=? ]

Let's correct the approach and find the correct composition of the function \( f(x) = x^2 - 2x \).<br /><br />Given:<br />\[ f(x) = x^2 - 2x \]<br /><br />We need to find \( (f \circ f)(x) \), which means we need to find \( f(f(x)) \).<br /><br />First, compute \( f(x) \):<br />\[ f(x) = x^2 - 2x \]<br /><br />Now, substitute \( f(x) \) into itself:<br />\[ f(f(x)) = f(x^2 - 2x) \]<br /><br />To find \( f(x^2 - 2x) \), we substitute \( x^2 - 2x \) into the function \( f(x) \):<br />\[ f(x^2 - 2x) = (x^2 - 2x)^2 - 2(x^2 - 2x) \]<br /><br />Now, let's simplify this step by step:<br /><br />1. Compute \( (x^2 - 2x)^2 \):<br />\[ (x^2 - 2x)^2 = x^4 - 4x^3 + 4x^2 \]<br /><br />2. Compute \( -2(x^2 - 2x) \):<br />\[ -2(x^2 - 2x) = -2x^2 + 4x \]<br /><br />3. Combine the results:<br />\[ f(x^2 - 2x) = x^4 - 4x^3 + 4x^2 - 2x^2 + 4x \]<br />\[ f(x^2 - 2x) = x^4 - 4x^3 + 2x^2 + 4x \]<br /><br />So, the composition \( (f \circ f)(x) \) is:<br />\[ (f \circ f)(x) = x^4 - 4x^3 + 2x^2 + 4x \]<br /><br />Therefore, the correct answer is:<br />\[ (f \circ f)(x) = x^4 - 4x^3 + 2x^2 + 4x \]