Question

Suppose that the functions s and t are defined for all real numbers x as follows. s(x)=6x∥t(x)=4x+1 Write the expressions for (s+t)(x) and (s\cdot t)(x) and evaluate (s−t)(2)

Answer 1

The sum of the functions is (s+t)(x) = 10x + 1, the product is (s·t)(x) = 24x² + 6x, and the value of (s−t) evaluated at x=2 is 3.

Step-by-step explanation:

The student has provided functions s(x) and t(x) and is asking to find the expressions for the sum (s+t)(x), product (s·t)(x), and the value of the difference (s−t) evaluated at x=2.

Firstly, to find the sum of the two functions, we add s(x) and t(x) together:

(s+t)(x) = s(x) + t(x) = 6x + (4x+1) = 10x + 1

Secondly, to find the product, we multiply s(x) by t(x):

(s·t)(x) = s(x) * t(x) = 6x * (4x+1) = 24x² + 6x

Finally, to evaluate (s−t)(2), we subtract t(x) from s(x) and plug in x=2:

(s−t)(x) = s(x) − t(x) = 6x − (4x+1)

(s−t)(2) = 6(2) − (4(2)+1) = 12 − (8+1) = 12 − 9 = 3