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

Question

s(x)=x-4

t(x)=4x²

Write the expressions for (s-t)(x)=? and (s+t)(x)=? and evaluate (s•t)(-3)=?

Answer 1

By definition of addition and subtraction, we can write

(s-t)(x)=s(x)-t(x)=x-4-4x²

(s_t)(x)=s(x)+t(x)=x-4+4x²

but composite of s and t, we define

(s•t)(x)=s(t(x))

Therefore,

(s•t)(-3)=s(t(-3))----(*)

Calculate t(-3)=4(-3)²=4(9)=36

by (*) implies (s•t)(-3)=s(t(-3))=s(36)=36-4=32