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renno2002p2li5j
Add like terms together..
-x^2 -x+6
............

The value of (f + g)(x) is [tex]6-x-x^2[/tex] and its domain is (-∞, ∞). This is obtained by applying the addition operation on the functions f(x) and g(x).

What are the operations on function?

Consider two functions f(x) and g(x)

Then,

Addition: (f+g)(x) = f(x)+g(x)

Subtraction: (f-g)(x) = f(x)-g(x)

Multiplication: (f×g)(x)=f(x) × g(x)

Division:(f/g)(x) = f(x)/g(x)

What is the domain of a function?

A domain of a function is a set of values that go into a function. If a function is represented by f(x)=y, then x- input and y-output. The domain of a function is the set of all possible inputs for the function.

The general formulas are used to find the domain of different types of functions. Where R represents the set of real numbers.

  • The domain of any polynomial (linear, quadratic, cubic, etc) function is R.
  • The domain of a square root function √x is x≥0.
  • The domain of an exponential function is R.
  • The domain of a logarithmic function is x>0.
  • To find the domain of a rational function y = f(x), set the denominator ≠ 0.

Calculating (f + g)(x) for the given functions:

Given functions are

f(x) = [tex]4-x^2[/tex],

g(x) = [tex]2-x[/tex]

Then,

(f + g)(x) = f(x) + g(x)

             = [tex]4-x^2+2-x[/tex]

             = [tex]6-x-x^2[/tex]

Thus, the values of (f + g)(x) are [tex]6-x-x^2[/tex].

Domain: all the values of R for x are possible for the function (f + g)(x)=[tex]6-x-x^2[/tex]. I.e., x: x ∈ (-∞, ∞).

Learn more about the operations of the functions here:

https://brainly.com/question/10727516

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