Suppose that the functions g and h are defined for all real numbers x as follows.
g(x) = 4x– 4
h(x) = x-5
Write the expressions for (g+h)(x) and (g-h)(x) and evaluate (g.h)(1).

Respuesta :

Answer:

See below in bold.

Step-by-step explanation:

(g + h)(x) = 4x - 4 + x - 5

= 5x - 9.

(g - h)(x) = 4x - 4 - (x - 5)  ( Note we put the x - 5 in parentheses)

= 4x - 4 - x + 5

=  3x + 1.

(g.h)(x) = (4x - 4)(x - 5)

so (g.h)(1) = (4(1) - 4)(1 - 5)

= 0 * -4

= 0.

The product of the functions will be (g·h)(x) = 4x² – 24x + 20. At x = 1, the product of the functions is zero.

What is a function?

A statement, principle, or policy that creates the link between two variables is known as a function.

The functions are given below.

g(x) = 4x – 4

h(x) = x – 5

Then the sum of the functions will be

(g + h)(x) = (4x – 4) + (x – 5)

(g + h)(x) = 4x – 4 + x – 5

(g + h)(x) = 5x – 9

Then the difference in the functions will be

(g – h)(x) = (4x – 4) – (x – 5)

(g – h)(x) = 4x – 4 – x + 5

(g – h)(x) = 3x + 1

Then the product of the functions will be

(g·h)(x) = (4x – 4)(x – 5)

(g·h)(x) = 4x² – 4x – 20x + 20

(g·h)(x) = 4x² – 24x + 20

At x = 1, then we have

(g·h)(x) = 4(1)² – 24(1) + 20

(g·h)(x) = 4 - 24 + 20

(g·h)(x) = 0

More about the function link is given below.

https://brainly.com/question/5245372

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