Hello!
The answer is:
B. [tex](f+g)(x)=3x^{2} -2x-1[/tex]
Why?
To solve the problem, we need to add/subtract like terms. The like terms are the terms that share the same variable and the same exponent.
For example:
[tex]x^{2} +3x^{2} +5x^{3}=4x^{2}+5x^{3}[/tex]
We were able to add the terms that were squared since both shares the same variable and the same exponent.
So, we are given the functions:
[tex]f(x)=-4x+3\\g(x)=3x^{2} +2x-4[/tex]
Now, we are asked to calculate (f+g)(x) which is also equal to f(x) + g(x).
Then, calculating we have:
[tex](f+g)(x)=(-4x+3)+(3x^{2} +2x-4)\\\\(f+g)(x)=3x^{2} -4x+2x+3-4\\\\(f+g)(x)=3x^{2} -2x-1[/tex]
Hence, the answer is:
B. [tex](f+g)(x)=3x^{2} -2x-1[/tex]
Have a nice day!
