Question

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

s(x)=x-3
t(x) = 4x+5
Write the expressions for (s+t)(x) and (s, t)(x) and evaluate (s t)(3).
(s + 1)(x) = 0 ----
(s – t)(x) = 0 ---
(sºt)(3) = 0 x|n|?---

Answer 1

The sum of the functions s and t, (s+t)(x), is 5x + 2; their difference, (s-t)(x), is -3x - 8; and the composition of s and t evaluated at x = 3, (s°t)(3), equals 14.

Step-by-step explanation:

The question involves the functions s(x) and t(x), which are defined as s(x) = x - 3 and t(x) = 4x + 5, respectively. To answer the questions:

• To find (s+t)(x), we need to add the two functions: (s+t)(x) = (x - 3) + (4x + 5) = 5x + 2.
• For (s-t)(x), we need to subtract the function t from s: (s-t)(x) = (x - 3) - (4x + 5) = -3x - 8.
• When composing functions, like (s°t)(x), you plug the function t(x) into the function s(x). Calculating (s°t)(3) gives us s(t(3)) = s(4(3) + 5) = s(17) = 17 - 3 = 14.

The solutions for the expressions and evaluations are:

• (s+t)(x) = 5x + 2,
• (s-t)(x) = -3x - 8,
• (s°t)(3) = 14.