Question

Suppose that the functions s and t are defined for all real numbers x as follows. s(x)=x-5 t(x) = 2x² Write the expressions for (t-s) (x) and (t.s) (x) and evaluate (t+s) (-2). (t-s) (x) (t.s) (x) (t+s) (-2)​

Answer 1

The expression for (t - s)(x) is 2x² - x + 5, and for (t · s)(x) is 2x³ - 10x². After evaluating (t + s)(-2), the result is 1.

Step-by-step explanation:

To find the expressions for (t - s)(x) and (t · s)(x), we have to perform the operations of subtraction and multiplication on the functions t(x) = 2x² and s(x) = x - 5.

For subtraction: (t - s)(x) = t(x) - s(x) = 2x² - (x - 5) = 2x² - x + 5.

For multiplication: (t · s)(x) = t(x) · s(x) = 2x² · (x - 5) = 2x³ - 10x².

Now to evaluate (t + s)(-2), we substitute x with -2 in both functions and then add them: t(-2) + s(-2) = 2(-2)² + ((-2) - 5) = 8 - 2 - 5 = 6 - 5 = 1.