1. F(x) = X + 2; G(x) = X2 - 4(f + G)(x) =​

answered • expert verified 1. f(x) = x + 2; g(x) = x2 - 4(f + g)(x) =​ See answer ProfAtika ProfAtika

OPERATION ON FUNCTION

(f + g)(x) = x² + x - 2.

1. Addition

Assume we have two functions, f(x) and g(x). The sum of these two functions is defined as,

• (f + g)(x) = f(x) + g(x)

2. Subtraction

Assume we have two functions, f(x) and g(x). The different relation between these two functions can be expressed as follows:

• (f - g)(x) = f(x) - g(x)

3. Multiplication

Assume we have two functions, f(x) and g(x) (x). The product of these two functions is defined as,

• (f . g)(x) = f(x) . g(x)

4. Division

Assume we have two functions, f(x) and g(x) (x). The division of these two functions is defined as,

• (f / g)(x) = f(x) / g(x), where g(x) ≠ 0

where x belongs to both f and g's domains We must specify g(x) ≠ 0 because we cannot divide by zero.

Function Composition

The process of combining two or more functions into a single function is called function composition.

The composition of functions f(x) and g(x), where g(x) treats first, is represented by f(g(x)) or (f ∘ g)(x).

GIVEN

• f(x) = x + 2
• g(x) = x² - 4

QUESTION

• (f + g)(x) =​ ...

Solution

• (f + g)(x) =​ f(x) + g(x)
• (f + g)(x) = x + 2 + x² - 4
• (f + g)(x) = x² + x - 2

Learn more about Function Composition here:

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