The functions f and g are defined by f(x) = 2x² and g(x) = (3x−2)/(x+1). Find fog(x).

The functions are defined as:

The notation $(f \circ g)(x)$ means $f(g(x))$. This involves substituting the entire function $g(x)$ into $f(x)$ wherever 'x' appears in $f(x)$.

Replace $x$ in $f(x) = 2x^2$ with $g(x) = \frac{3x-2}{x+1}$:

Square the fraction:

Expand the numerator $(3x-2)^2$ and the denominator $(x+1)^2$:

Substitute these expanded forms back into the expression:

Multiply the numerator by 2:

The composite function is: