Question

MATH HELP PLEASE!!!!!!!!!!!!!

Answer 1

The answer is:  [C]:  " f ⁻¹(x) = (5x + 3) / 2 " .
______________________________________________________
Explanation:
______________________________________________________
Given:  "f(x) = (2x - 3) / 5 ;  which is the "inverse" of:  " f(x)" ?

Substitute "y" for "f(x)" :

y = (2x - 3) / 5 ; 

Replace "x" with "y"; and "y" with "x" ; and rewrite:

x = (2y - 3) / 5 ; 

Now,  solve for "y" , in term of  "x'  ;

Multiply each side of the equation by "5" 

5 * x = 5 * { (2y - 3) / 5 } ; 

to get:

5x = 2y - 3 ;  

Add "3" to each side of the equation:

5x + 3 = 2y - 3 + 3 ; 

to get:  5x + 3 = 2y ; 

↔  2y = 5x + 3 ; 

Divide each side of the question by "2" ; 
      to isolate "y" on one side of the equation; & to solve for "y" in terms of "x" ; 

   → 2y / 2 = (5x + 3) / 2 ; 

to get:  y = (5x + 3) / 2 ;  

Replace the "y" with:  " f ⁻¹(x) " ; 

and rewrite:

" f ⁻¹(x) = (5x + 3) / 2 " ;

→  which is:  "Answer choice:  [C]:  " f ⁻¹(x) = (5x + 3) / 2 " .
__________________________________________________