Question

suppose that the functions s and t are defined for all real numbers x as follows. s(x)=3x-2 t(x)=4x. Write the expressions for (s+t)(x) and (s*t)(x) and evaluate (s-t)(-2).

Answer 1

Given the functions:

s(x) = 3x - 2

t(x) = 4x

Let's find the following:

• (s + t)(x):

Here we are to add both functions together

(s + t)(x) = (3x - 2) + 4x

= 3x - 2 + 4x

= 3x + 4x - 2

= 7x - 2

• (s * t)(x):

Here, we are to multiply both functions

(s * t)(x) = (3x - 2)(4x)

= 3x(4x) - 2(4x)

= 12x² - 8x

• (s - t)(-2):

Here, let's subtract both functions and input -2 for x.

s(-2) - t(-2) = (3(-2) - 2)) - (4(-2))

= (-6 - 2) - (-8)

= ( -8) - (-8)

= -8 + 8 = 0

ANSWER:

(s + t)(x) = 7x - 2

(s * t)(x) = 12x² - 8x

(s - t)(-2) = 0