The answer is: " f ⁻¹(x) = 
+ 5 " .
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Explanation:
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Given the function: " f(x) = 2x <span>− 10 " ; Find the "inverse function" .
Let "f(x)" be represented by "y" ; and rewrite:
y = 2x </span><span>− 10 ;
Change the "y" to an "x" ; and change to "x" to a "y" ; as follows:
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x = 2y </span><span>− 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:
___________________________________________________
" x = 2y </span><span>− 10 " ;
Add "10" to each side of the equation; as follows:
x + 10 = 2y </span><span>− 10 + 10 ;
to get:
x + 10 = 2y ;
</span>↔ 2y = x + 10 ;
<span>
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" ;
</span>→ 2y / 2 = (x + 10) / 2 ;
<span>
to get:
</span>→ y = (x/2) + (10/2) ;
→ y = (x/2) + 5 ;
<span>
Now, rewrite the equation, by substituting: " f </span>⁻¹(x) " ; in place of the "y" ; to indicate that this function is an "inverse function; as follows:
→ " f ⁻¹(x) = + 5 " .
______________________________________________________
The answer is: " f ⁻¹(x) = + 5 " .
_______________________________________________________
____________________________________________________
Explanation:
____________________________________________________
Given the function: " f(x) = 2x <span>− 10 " ; Find the "inverse function" .
Let "f(x)" be represented by "y" ; and rewrite:
y = 2x </span><span>− 10 ;
Change the "y" to an "x" ; and change to "x" to a "y" ; as follows:
___________________________________________________
x = 2y </span><span>− 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;
___________________________________________________
We have:
___________________________________________________
" x = 2y </span><span>− 10 " ;
Add "10" to each side of the equation; as follows:
x + 10 = 2y </span><span>− 10 + 10 ;
to get:
x + 10 = 2y ;
</span>↔ 2y = x + 10 ;
<span>
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" ;
</span>→ 2y / 2 = (x + 10) / 2 ;
<span>
to get:
</span>→ y = (x/2) + (10/2) ;
→ y = (x/2) + 5 ;
<span>
Now, rewrite the equation, by substituting: " f </span>⁻¹(x) " ; in place of the "y" ; to indicate that this function is an "inverse function; as follows:
→ " f ⁻¹(x) =
______________________________________________________
The answer is: " f ⁻¹(x) =
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