f(x)=8-4x+x^3

Question

g(x)=2x^2+5x-1
find f(x)+g(x)
a)10x^2+x-x^3
b)x^3+2x^2+x+7
c)x^3+2x^2+9x-1
d)x^3+2x^2-x+7

Answer 1

To find \( f(x) + g(x) \), we need to add the two functions \( f(x) = 8 - 4x + x^3 \) and \( g(x) = 2x^2 + 5x - 1 \).

Let's perform the addition:

\[ f(x) + g(x) = (8 - 4x + x^3) + (2x^2 + 5x - 1) \]

Now, combine like terms:

1. Cubic term: \( x^3 \)
2. Quadratic term: \( 2x^2 \)
3. Linear term: \( -4x + 5x = x \)
4. Constant term: \( 8 - 1 = 7 \)

Putting it all together, we get:

\[ f(x) + g(x) = x^3 + 2x^2 + x + 7 \]

Thus, the result is given by option (b) \( x^3 + 2x^2 + x + 7 \).