Question

Suppose that the functions fand g are defined for all real numbers x as follows

f(x)=x-3
g(x)=3x+2
Write the expressions for (f-g)(x) and (f.g)(x) and evaluate (f+g) (3).
(-8)(x)=
(f⋅g)(x) =
(f+g)(3)=
ㅁ
X
5

Answer 1

(f - g)(x):

We proceed to subtract the two functions.

`(f - g)(x) \: = \: (x \: - \: 3) \: - \: (3x \: + \: 2)`

`(f - g)(x) \: = \: \boxed{ \bold{- 2x \: - \: 5}}`

(f • g)(x):

We proceed to multiply the functions.

`(f \: * \: g)(x) \: = \: (x \: - \: 3) \: * \: (3x \: + \: 2)`

`(f \: * \: g)(x) \: = \underline{\: x \: * \: 3x \: + \: 2x \: - \: 3 \: * \: 3x \: - \: 3 \: * \: 2}`

`(f \: * \: g)(x) \: = \: {3x}^(2) \: + \: 2x \: - \: 9x \: - \: 6`

`(f \: * \: g)(x) \: = \boxed{ \bold{ \: {3x}^(2) \: - \: 7x \: - \: 6}}`

(f + g)(x):

We proceed to add the functions, substituting the "3" for the unknown "x".

`(f\: + \: g)(3) \: = \: (3 \: - \: 3) \: + \: 3(3) \: + \: 2`

`(f \: + \: g)(3) \: = \: 0 \: + \: 9 \: + \: 2`

`(f \: + \: g)(3) \: = \: \boxed{ \bold{11}}`

Cheers!!