Answer :

To find [tex]\((f+g)(x)\)[/tex] for the given functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex], we need to add the two functions together. Here, the given functions are:

[tex]\[ f(x) = 10x^5 - 3x^4 - 9x^3 + 8x \][/tex]
[tex]\[ g(x) = -x^5 - 5x^4 - 9x^2 - 12 \][/tex]

Now, let's add [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] term by term:

1. Combine the [tex]\( x^5 \)[/tex] terms:
[tex]\[ 10x^5 + (-x^5) \][/tex]
[tex]\[ = 9x^5 \][/tex]

2. Combine the [tex]\( x^4 \)[/tex] terms:
[tex]\[ -3x^4 + (-5x^4) \][/tex]
[tex]\[ = -8x^4 \][/tex]

3. Combine the [tex]\( x^3 \)[/tex] terms:
[tex]\[ -9x^3 + 0 \][/tex]
[tex]\[ = -9x^3 \][/tex]

4. Combine the [tex]\( x^2 \)[/tex] terms:
[tex]\[ 0 + (-9x^2) \][/tex]
[tex]\[ = -9x^2 \][/tex]

5. Combine the [tex]\( x \)[/tex] terms:
[tex]\[ 8x + 0 \][/tex]
[tex]\[ = 8x \][/tex]

6. Combine the constant terms:
[tex]\[ 0 + (-12) \][/tex]
[tex]\[ = -12 \][/tex]

Putting it all together, we get:

[tex]\[ (f+g)(x) = 9x^5 - 8x^4 - 9x^3 - 9x^2 + 8x - 12 \][/tex]

So, the function [tex]\((f+g)(x)\)[/tex] is:

[tex]\[ (f+g)(x) = 9x^5 - 8x^4 - 9x^3 - 9x^2 + 8x - 12 \][/tex]

Thanks for taking the time to read Find tex f g x tex for the given functions tex f x 10x 5 3x 4 9x 3 8x tex tex g x x. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada