If $f(x) = x^3 - 6x^2 + 3x - 4$, $g(x) = x^3 + 5x^2 + 9x - 2$, then find the constant term of $f(g(x))$.
+499 Hey guest!
Since we know that g(x)=x3+5x2+9x−2, we already have part of the desired expression of f(g(x)).
The question then becomes reduced to:
f(x3+5x2+9x−2)
since f(x)=x3−6x2+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 x3+5x2+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
