Final answer:
The student needs to combine the functions f(x) = 2x + 3 and g(x) = x^2 - 1 to find specific values and possibly sketch the graphs of these combined functions. This involves algebraic operations such as addition, subtraction, and function composition. An example of finding a value for (f + g)(x) when x=1 is also provided.
Step-by-step explanation:
The student is asking to find the values of certain combined functions. When we combine the functions f(x) = 2x + 3 and g(x) = x^2 - 1, we can create new functions through operations such as addition, subtraction, multiplication, and composition. For instance, (f + g)(x) would be f(x) + g(x), and (f - g)(x) would be f(x) - g(x). To find specific values, we would substitute a particular x value into these combined functions and calculate the result.
As an example, let's calculate (f + g)(1):
(f + g)(1) = f(1) + g(1) = (2 * 1 + 3) + (1^2 - 1) = 5 + 0 = 5.
Therefore, when we combine f(x) and g(x) by addition and evaluate at x=1, we get a value of 5.
To sketch a graph of these functions, you can create a table of (x,y) data pairs for a range of x values and then plot each point on a coordinate plane. This visual representation would show how the y value changes as a function of x for each combined function.