If f(x)=x2−x and g(x)=2x−1, then fog(x)= ....
Explanation
Given the functions f(x)=x2−x and g(x)=2x−1. We are asked to find the composite function (fog)(x).
(fog)(x)=f(g(x))
We substitute g(x) into the function f(x).
(fog)(x)=f(2x−1)
(fog)(x)=(2x−1)2−(2x−1)
Next, we expand the quadratic form and simplify the equation.
(fog)(x)=(4x2−4x+1)−(2x−1)
(fog)(x)=4x2−4x+1−2x+1
(fog)(x)=4x2−6x+2
So, the value of (fog)(x) is 4x2−6x+2.