Question

If p(x) = x² - 1 and q(x) = 5(x-1), which expression is equivalent to (p-q)(x)?

a. 0.5(x - 1) - x - 1
b. (5x - 1)-(x² - 1)
c. (x² - 1)-5(x - 1)
d. (x² - 1) - 5x - 1

Answer 1

The equivalent expression for (p-q)(x) is c. (x² - 1)-5(x - 1) which simplifies to x² - 5x + 4.

Step-by-step explanation:

To find the expression equivalent to (p-q)(x), we begin by substituting the given functions into the expression. The function p(x) is given as x² - 1 and q(x) is given as 5(x-1). Therefore, (p-q)(x) can be written as:

p(x) - q(x) = (x² - 1) - 5(x - 1)

Now, distribute the negative through the parentheses:

x² - 1 - 5x + 5

Combine like terms:

x² - 5x + 4

This simplifies the expression to x² - 5x + 4, which matches the expression in option c. Therefore, option c is the correct choice: (x² - 1)-5(x - 1).