What is $$ (f-g)(x) $$ ? $$ f(x)=2 x+5 $$ $$ g(x)=-3 x^{2}+4 x $$ Write your answer as a polynomial or a rational function in simplest form.

Question

UpStudy AI · Accepted Answer

To find $$ (f - g)(x) $$, subtract the function $$ g(x) $$ from $$ f(x) $$:

$$
f(x) = 2x + 5
$$
$$
g(x) = -3x^2 + 4x
$$

Subtracting $$ g(x) $$ from $$ f(x) $$:

$$
(f - g)(x) = f(x) - g(x) = (2x + 5) - (-3x^2 + 4x)
$$

Simplify the expression:

$$
(f - g)(x) = 2x + 5 + 3x^2 - 4x = 3x^2 - 2x + 5
$$

**Final Answer:**

$$
(f - g)(x) = 3x^{2} - 2x + 5
$$
$$ (f - g)(x) = 3x^{2} - 2x + 5 $$

What is ?

Write your answer as a polynomial or a rational function in simplest form.