Use the function to answer the question.
f(x) = 5x - 10
what is the value of f^–1 (–3)?

The answer is: 7/5 ; or write as: 1⅖ ; or write as 1.4 .


Explanation:

Given: f(x) = 5x − 10; Find f⁻¹(-3).

→ Find:  f ⁻¹(x) = 5x − 10 ; 

→ Write: f(x) = 5x − 10;  as:

→ y = 5x − 10 ; 

→ Replace the "x" with the "y", and the 'y" with the "x"; and Rewrite:

→ x = 5y − 10 ; 

Now, rewrite the ABOVE equation in "slope-intercept form"; or "y = mx + b"; that is: with "y" as a "stand-alone" variable on the left-hand side;

We have:  x = 5y − 10 ;  

Subtract "x" ; and subtract "5y" ; from EACH side of the equation:

→ x − x − 5y = 5y − 10 − x − 5y ; 

→  -5y = -10 − x ;  Multiply the ENTIRE EQUATION (both sides) by "-1" ;

→  -1* {-5y = -10 − x} ;

→ 5y = 10 + x ; ↔ 5y = x + 10 ; 

→ Now, divide EACH side of the equation by "5" ;

→ 5y / 5= (x + 10) /5 ;

→  y = x/5  + 10/5 ; 

→ y = x/5 + 2 ; Now we can replace "y" with:  f⁻¹(x) ;

→ f⁻¹(x) = x/5 + 2

Now, to find: f⁻¹(-3) ; we plug "3" for "x" in this [inverse] function:

→ f⁻¹(-3) = (-3)/5 + 2 = -⅗ + 2 =  7/5 ; or write as: 1⅖ ; or write as 1.4 .
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