Question

Suppose that the functions s and t are defined for all real numbers x as follows.s (x) = 4x + 4t(x) = 3xWrite the expressions for (s + t)(x) and (s – t)(x) and evaluate (s.t)(3).(s + 1)(x) = 1(s - 1)(x) = 1(sot) (3) = 1Х?

Answer 1

(s+t)(x) = 7x+4

(s-t)(x) = x + 4

s(t(3)) = 40

Explanation:

We are given the following function:

s(x) = 4x + 4

t(x) = 3x

(s + t)(x)

Addition of functions: We add the common terms:

So

(s+t)(x) = 4x + 4 + 3x = 4x + 3x + 4 = 7x + 4

(s-t)(x)

Same logic as above, just now we subtract

(s-t)(x) = 4x + 4 - 3x = 4x - 3x + 4 = x + 4

Composite:

s(t(x)) = s(3x) = 4(3x) + 4 = 12x + 4

When x = 3

s(t(3)) = 12*3 + 4 = 40