(f + g)(x) is a composite function of f(x) and g(x), and it is represented by graph (c)
The functions are given as:
[tex]\mathbf{f(x) = -x^2 + 3x + 5}[/tex]
[tex]\mathbf{g(x) = x^2 + 2x}[/tex]
To calculate (f + g)(x), we make use of the following formula
[tex]\mathbf{(f + g)(x) = f(x) + g(x)}[/tex]
So, we have:
[tex]\mathbf{(f + g)(x) = -x^2 + 3x + 5 + x^2 + 2x}[/tex]
Collect like terms
[tex]\mathbf{(f + g)(x) = x^2-x^2 + 3x+ 2x + 5 }[/tex]
Evaluate the like terms
[tex]\mathbf{(f + g)(x) = 5x + 5}[/tex]
The above function is a linear function.
A linear function is represented as:
[tex]\mathbf{y = mx + c}[/tex]
Where m represents the slope, and c represents the y-intercept
So, by comparison:
[tex]\mathbf{m = 5}[/tex]
[tex]\mathbf{c = 5}[/tex]
The graph that has a slope of 5, and a y-intercept of 5 is graph (c)
Hence, graph (c) represents (f + g)(x)
Read more about composite functions at:
https://brainly.com/question/20379727
