Question

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

Answer 1

The answer is: " f ⁻¹(x) =
`(x)/(2)` + 5 " .
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Step-by-step 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) =
`(x)/(2)` + 5 " .
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The answer is: " f ⁻¹(x) =
`(x)/(2)` + 5 " .
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Answer 2

h(x) = 1/2x – 5 i believe