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)=

Respuesta :

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


[tex] (s+t)(x) = s(x)+t(x) = (4x+4)+(x-5) = 5x-1 [/tex]

[tex] (s-t)(x) = s(x)-t(x) = (4x+4)-(x-5) = 3x+9 [/tex]


Similarly, the multiplication is defined as


[tex] (s\cdot t)(x) = s(x) \cdot t(x) = (4x+4)(x-5) [/tex]


To compute [tex](s\cdot t)(1)[/tex], substitute every occurrence of x with 1:


[tex] (s\cdot t)(1) = (4+4)(1-5) = 8\cdot (-4) = -32 [/tex]