(1)  To calculate f(7), you need to find a value of x such that 3x-2 = 7.


     You can do it in one line:  3x-2 = 7  ====>  3x = 7+2 = 9  ====>  x = 9/3 = 3.


     Then f(7) = f(3*3-2) = 3 + 5 = 8,  according the given definition of the function f.




(2)  To find  ,  you first find "x" from equation x+5 = 7  (left side of the definition of the function f).


     You do it in one line:  x = 7-5 = 2.


     Then you calculate  3x-2  at  x= 2,  and you get  the value  3*2-2 = 6-2 = 4.


     So, f(4) = 7,  which implies    = 4.




(3)  Finally,   +  = 8 + 4 = 12.

(1)  You are given  f(3x-2) = x + 5.


    Introduce new variable  t = 3x-2   and  express  x  via t.


    You will get  x = .


    Thus  f(t) = x + 5 =      (*)

        is the expression (definition) of the given function as the function of "t".


     Now  f(7) =  =  = 3 + 5 = 8.



(2)  To find  ,  you need to find which number "t" gives the value of 7 to the expression  , which is left side of (*).


     So, you solve the equation   = 7,

     and you do it in one line   = 7 - 5 = 2  ====>  t+2 = 3*2  ====>  t = 3*2 -2 = 4.


     Thus,   = 4,  and you get the same answer as in the first solution above:



      +  = 8 + 4 = 12.