Question

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

s(x)=4x+4
t(x)=x-5


Write the expressions for (s-t)(x) and (s+t)(x) and evaluate (s*t)(1)

(s-t)(x)=
(s+t)(x)=
(s*t)(1)=

Answer 1

To compute the sum/difference of two function, simply sum/subract their expressions:

`(s+t)(x) = s(x)+t(x) = (4x+4)+(x-5) = 5x-1`

`(s-t)(x) = s(x)-t(x) = (4x+4)-(x-5) = 3x+9`

Similarly, the multiplication is defined as

`(s\cdot t)(x) = s(x) \cdot t(x) = (4x+4)(x-5)`

To compute
`(s\cdot t)(1)`, substitute every occurrence of x with 1:

`(s\cdot t)(1) = (4+4)(1-5) = 8\cdot (-4) = -32`