Question

Suppose that the functions f and g are defined for all real numbers x as follows. f(x) = 4x-1 g(x) = 3x write the expressions for (f-g)(x) and (f+g)(x) and evaluate (f * g)(-1).

Answer 1

The result of the operations between the two functions are listed below:

1. (f - g) (x) = x - 1
2. (f + g) (x) = 7 · x - 1
3. (f · g) (- 1) = 15

How to perform operations between real functions

In this question we find two functions defined as two linear equations, with which we must make three kinds of operations and evaluate the resulting expression in the third case. The addition, subtraction and multiplication of two functions are defined below:

Addition

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

Subtraction

(f - g) (x) = f(x) - g(x)

Multiplication

(f · g) (x) = f(x) · g(x)

Now we proceed to find the result for each case:

(f - g) (x) = (4 · x - 1) - (3 · x)

(f - g) (x) = 4 · x - 1 - 3 · x

(f - g) (x) = x - 1

(f + g) (x) = (4 · x - 1) + 3 · x

(f + g) (x) = 7 · x - 1

(f · g) (x) = (4 · x - 1) · (3 · x)

(f · g) (x) = 12 · x² - 3 · x

(f · g) (- 1) = 12 · (- 1)² - 3 · (- 1)

(f · g) (- 1) = 12 + 3

(f · g) (- 1) = 15

To learn more on operations for functions: brainly.com/question/14996787

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