Answer:
f⁻¹ (x) =
;
___________________________________________________________
→ or; write as:
f⁻¹ (x) =
.
___________________________________________________________Step-by-step explanation:___________________________________________________________Given: "
f(x) = 5x " ; Find: "
f⁻¹ (x) " ;
Note that: "
f⁻¹ (x) " is the "
inverse function".
___________________________________________________________Given: "
f(x) = 5x " ;
Rewrite as: "
y = 5x" ;
To solve for the "inverse function" ; exchange "
x" with "
y"; and "
y" with "
x" ; and rewrite:
___________________________________________________________ → x = 5y ;
___________________________________________________________Now, isolate "
y" on one side of the equation; & solve for "
y" ; in terms of "
x" ;
→ x = 5y ;
↔ 5y = x ;
Divide EACH SIDE of the equation by "
5" ; as follows:
→ 5y / 5 = x / 5 ;
to get: ___________________________________________________________ → y = x / 5 ;
___________________________________________________________Now, replace the "
y" ; with: "
f⁻¹ (x) " ;
→ and rewrite; as follows:___________________________________________________________ → f⁻¹ (x) =
;
___________________________________________________________→ or, write as: ___________________________________________________________ → f⁻¹ (x) =
.
___________________________________________________________