If $f(x) = x^3 - 6x^2 + 3x - 4$, $g(x) = x^3 + 5x^2 + 9x - 2$, then find the constant term of $f(g(x))$.
+500 Hey guest!
Since we know that \(g(x) = x^3+5x^2+9x-2\), we already have part of the desired expression of f(g(x)).
The question then becomes reduced to:
\(f(x^3+5x^2+9x-2)\)
since \(f(x) = x^3-6x^2+3x-4\), this may seem really complicated at first glance. However, remember what they ask us for; the constant term. That means we can ignore everything except for the constant term of the expression \(x^3+5x^2+9x-2\), which is -2.
Plugging -2 into the function \(f(x)\), we get:
\(f(-2) = (-2)^3-6(-2)^2+3(-2)-4 = -8-24-6-4 =-42\)
Thus, the constant term of the function f(g(x)) is -42
