Suppose that the functions g and h are defined for all real numbers x as follows. gx = x − 3x
hx = 5x + 2
Write the expressions for (g - h)(x) and (g * h)(x) and evaluate (g + h)(−2).

Step-by-step explanation:

Given the functions g(x) = x − 3x  and h(x) = 5x + 2, we are to calculatae for the expression;

a) (g - h)(x)  an (g * h)(x)

(g - h)(x)  = g(x) - h(x)

(g - h)(x)  = x − 3x -(5x+2)

(g-h)(x) = x-3x-5x-2

(g-h)(x) =-7x-2

b)  (g * h)(x) =  g(x) * h(x)

 (g * h)(x)  = (x − 3x )(5x+2)

(g * h)(x) = 5x²+2x-15x²-6x

(g * h)(x) = 5x²-15x²+2x-6x

(g * h)(x) = -10x²-4x

c) To get (g + h)(−2), we need to first calculate (g + h)(x) as shown;

 (g + h)(x)  an (g * h)(x)

(g + h)(x)  = g(x) +h(x)

(g + h)(x)  = x − 3x + (5x+2)

(g+h)(x) = x-3x+5x+2

(g+h)(x) =3x+2

Substituting x = -2 into the resulting function;

(g+h)(-2) = 3(-2)+2

(g+h)(-2) = -6+2

(g+h)(-2) = -4

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|