Question

f(x)=x^2-3x+9
g(x)=3x^3+2x^2-4x-9
find (f-g)(x)
a)3x^3-x^2-x
b)-3x^3-x^2+x+18
c)3x^3+x^2-x-18
d)3x^3+3x^2-7x

Answer 1

To find \((f - g)(x)\), we need to subtract \(g(x)\) from \(f(x)\).

Given:
\[
f(x) = x^2 - 3x + 9
\]
\[
g(x) = 3x^3 + 2x^2 - 4x - 9
\]

Now, let's compute \((f - g)(x)\):

\[
(f - g)(x) = f(x) - g(x)
\]
\[
= (x^2 - 3x + 9) - (3x^3 + 2x^2 - 4x - 9)
\]

Distributing the negative sign to \(g(x)\):
\[
= x^2 - 3x + 9 - 3x^3 - 2x^2 + 4x + 9
\]

Now, combine like terms:
- The \(x^3\) term: \(-3x^3\)
- The \(x^2\) terms: \(x^2 - 2x^2 = -x^2\)
- The \(x\) terms: \(-3x + 4x = x\)
- The constant terms: \(9 + 9 = 18\)

Putting it all together:
\[
(f - g)(x) = -3x^3 - x^2 + x + 18
\]

Thus, the answer corresponds to option:
\[
\boxed{-3x^3 - x^2 + x + 18}
\]