determine if the two functions f and g are inverses of each other algebraically. If not, why?

f(x)=2x+3/4x-3 ; g(x) = 3x+3/4x-2

a:
no, (f o g)(x)= x+2/3
yes
no, (f o g)(x)=3x

f(x) = -x^3+2 ; g(x) = 3(cubedroot)x-2/2

a:
no, (f o g)(x)= x-14/8
yes
no, (fog)(x)=3-x/2

f(x)=-2x+4/2-5x ; g(x) = 4-2x/5-2x

a:
no, (f o g)(x)= -2x+6/3x-5
no, (f o g)(x)= -6x+6/3x-5
yes.

(the number say ex. g(x) = 4-2x / the "/" is a fraction unit. first unit over the other as provided. any help appreciated thank you <3)

Respuesta :

Answer:

N0 (f o g) x = 3x.

Step-by-step explanation:

If they are inverses of each other the f o g will equal x.

f o g  =  2(3x +3/ (4x - 2)  + 3  /    4(3x + 3)/(4x - 2) - 3)

=  2(3x + 3)+ 3(4x - 2)                4x - 2

   ---------------------------  *    ----------------------------

            4x - 2                     4(3x + 3) - 3(4x - 2)

      6x + 12x

=   ----------------

        12 - 6

= 3x.

So they are not inverses.

 

Answer:

1) yes

2) no, (fog)(x)=3-x/2

3) no, (f o g)(x)= -2x+6/3x-5