Question

What’s the inverse of the function f(x) = 2x - 10

Answer 1

The answer is:  " f ⁻¹(x)  = $\frac{x}{2}$  + 5 " . 
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Explanation:
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Given the function:  " f(x) = 2x − 10 " ;  Find the "inverse function" .

Let "f(x)" be represented by "y" ; and rewrite:

    y = 2x − 10 ; 

Change the "y" to an "x" ;  and change to "x" to a "y" ; as follows:
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    x = 2y − 10 ; 

Now, rewrite this equation, in "slope-intercept form";  that is;  "y = mx + b" ; 

To do this, start by solving THIS equation for "y"; in terms of "x" ; with "y" as an "isolated variable" on the "left-hand side" of the equation; 
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 We have: 
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   " x = 2y − 10 " ; 

Add "10" to each side of the equation; as follows:

    x + 10 = 2y − 10 + 10 ; 

to get:

     x + 10 = 2y ; 

↔  2y = x + 10 ;

Now, divide each side of the equation by "2" ; 
       to isolate "y" on one side of the equation (as a single variable); 
       & to solve for "y" ; 

→  2y / 2 = (x + 10) / 2 ; 

to get: 

→    y = (x/2)  + (10/2) ; 

→    y = (x/2) + 5 ; 

Now, rewrite the equation, by substituting:  " f ⁻¹(x) " ;  in place of the "y" ;                     to indicate that this function is an "inverse function; as follows:
 
→   " f ⁻¹(x)  = $\frac{x}{2}$  + 5 " . 
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The answer is:  " f ⁻¹(x)  = $\frac{x}{2}$  + 5 " . 
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Answer 2

H(x) = 1/2x – 5  i believe