Question

Suppose that the functions s and t are defined for all real numbers. x as follows:

s(x) = 2x - 4
t(x) = 6x
Write the expressions for (s + t)(x) and (s * t)(x) and evaluate(s - t)(-1).

Answer 1

The expressions for (s + t)(x) and (s * t)(x) are 8x - 4 and 12x^2 - 24x, respectively. To evaluate (s - t)(-1), we substitute -1 into both functions, ultimately finding that (s - t)(-1) equals 0.

Step-by-step explanation:

The functions s(x) and t(x) are given as s(x) = 2x - 4 and t(x) = 6x. To find the expressions for the sum, (s + t)(x), and the product, (s \* t)(x), of the functions, you would add and multiply the functions respectively.

For the sum of the functions, you add together the values of s(x) and t(x), which yields (s + t)(x) = 2x - 4 + 6x = 8x - 4. The product of the functions is found by multiplying together the values of s(x) and t(x), resulting in (s \* t)(x) = (2x - 4)(6x) = 12x2 - 24x.

When evaluating (s - t)(-1), we substitute -1 into the expressions for s(x) and t(x) and then find the difference. This yields s(-1) = 2(-1) - 4 = -2 - 4 = -6 and t(-1) = 6(-1) = -6, therefore, (s - t)(-1) = s(-1) - t(-1) = -6 - (-6) = 0.