Question

Given f(x) = x - 2 and g(x) = x^2 - x, determine (f+g)(4), if it exists.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. (f+g)(4) = ? (Simplify your answer.)
B. The value for (f+g)(4) does not exist.

Answer 1

To evaluate (f+g)(4), you add the functions f(x) and g(x) and then substitute x with 4. The result for (f+g)(4) is 14.

Step-by-step explanation:

To find the value of the function (f+g)(x), you simply add the two functions f(x) and g(x) together and then evaluate the resulting function at x=4. Let's go through the process step by step:

• Firstly, take the given functions f(x) = x - 2 and g(x) = x^2 - x.
• Add these two functions together: (f+g)(x) = f(x) + g(x) = (x - 2) + (x^2 - x).
• Simplify the expression: (f+g)(x) = x - 2 + x^2 - x = x^2 - 2.
• Substitute x with 4 and evaluate: (f+g)(4) = 4^2 - 2 = 16 - 2 = 14.

The value of (f+g)(4) is 14. Hence, the correct choice is A.