The answer is: " f ⁻¹(x) = [tex] \frac{1}{2} [/tex] x + 5 " .
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Explanation:
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Given the function: " f(x) = 2x − 10 " ; Find the inverse of this function ;
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Explanation:
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Let: f(x) = y = 2x − 10 ;
Replace "y" with "x" ; and "x" with "y" ;
x = 2y − 10 ;
Now, solve for "y" ; in terms of "x" ; in "slope-intercept format" ;
x = 2y − 10 ;
↔ 2y − 10 = x ;
Now, add "10" to each side of the equation ;
2y − 10 + 10 = x + 10 ;
to get:
2y = x + 10 ;
Now, divide EACH SIDE of the equation by "2" ;
to isolate "y" on one side of the equation; & to solve for "y" in terms of "x" ;
2y/2 = (x + 10) / 2 ;
to get:
y = (x + 10)/2 ;
→ y = (x/2) + (10/2) ;
→ y = (1/2)x + 5 ;
Now replace: "y" ; with: " f ⁻¹(x)" ; and rewrite:
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→ " f ⁻¹(x) = [tex] \frac{1}{2} [/tex] x + 5 " .
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