Answer :
To find [tex]\((g+f)(x)\)[/tex], we need to add the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] together.
1. Start with the given functions:
[tex]\[
f(x) = 4x^2 + 3x^2 - 5x + 20
\][/tex]
[tex]\[
g(x) = 9x^3 - 4x^2 + 10x - 55
\][/tex]
2. Add [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[
(g+f)(x) = g(x) + f(x)
\][/tex]
[tex]\[
= (9x^3 - 4x^2 + 10x - 55) + (4x^2 + 3x^2 - 5x + 20)
\][/tex]
3. Combine like terms:
- The [tex]\(x^3\)[/tex] term: [tex]\(9x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(-4x^2 + 4x^2 + 3x^2 = 3x^2\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(10x - 5x = 5x\)[/tex]
- The constant terms: [tex]\(-55 + 20 = -35\)[/tex]
4. Put it all together:
[tex]\[
(g+f)(x) = 9x^3 + 3x^2 + 5x - 35
\][/tex]
Therefore, the simplified function is [tex]\((g+f)(x) = 9x^3 + 3x^2 + 5x - 35\)[/tex]. If there was an error in calculation during an earlier step, do verify the provided expression for correctness.
1. Start with the given functions:
[tex]\[
f(x) = 4x^2 + 3x^2 - 5x + 20
\][/tex]
[tex]\[
g(x) = 9x^3 - 4x^2 + 10x - 55
\][/tex]
2. Add [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[
(g+f)(x) = g(x) + f(x)
\][/tex]
[tex]\[
= (9x^3 - 4x^2 + 10x - 55) + (4x^2 + 3x^2 - 5x + 20)
\][/tex]
3. Combine like terms:
- The [tex]\(x^3\)[/tex] term: [tex]\(9x^3\)[/tex]
- The [tex]\(x^2\)[/tex] terms: [tex]\(-4x^2 + 4x^2 + 3x^2 = 3x^2\)[/tex]
- The [tex]\(x\)[/tex] terms: [tex]\(10x - 5x = 5x\)[/tex]
- The constant terms: [tex]\(-55 + 20 = -35\)[/tex]
4. Put it all together:
[tex]\[
(g+f)(x) = 9x^3 + 3x^2 + 5x - 35
\][/tex]
Therefore, the simplified function is [tex]\((g+f)(x) = 9x^3 + 3x^2 + 5x - 35\)[/tex]. If there was an error in calculation during an earlier step, do verify the provided expression for correctness.
