Question

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

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


Write the expressions for
(t*s)(x)
(t - s)(x)
and evaluate (t + s)(- 2)

Answer 1

-5

Explanation:

The expression for the composition of functions t and s, (t*s)(x), is obtained by substituting the output of s(x) into t(x). So,

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

The expression for the difference of functions t and s, (t - s)(x), is obtained by subtracting the output of s(x) from t(x). So,

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

To evaluate (t + s)(-2), we need to add the outputs of t(-2) and s(-2).

t(-2) = 3(-2) + 3 = 3

s(-2) = 4(-2) = -8

So, (t + s)(-2) = t(-2) + s(-2) = 3 + (-8) = -5.