Answer: " f⁻¹(x) = (x-1)/2 "; or, write as:
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" f⁻¹(x) = (x/2) - (1/2) " .
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Step-by-step explanation:
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Given: f(x) = 2x + 1 ; Find the inverse:
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1) Rewrite as y = 2x + 1 ;
2) Replace the "x" with "y" ; and the "y" with "x" ; and rewrite:
x = 2y + 1 ;
3) Now, "solve"; with "y" standing alone as a single, isolated variable on the left side of the equation, with an "equals" sign following the "y" :
x = 2y + 1 :
Subtract "1" from each side of the equation:
x - 1 = 2y + 1 - 1 ;
to get:
x - 1 = 2y ;
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↔ Rewrite as :
2y = x - 1 ;
Now, divide each side of the equation by "2" ;
to isolate "y" on the left-hand side of the equation;
& to solve in terms of "y":
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2y / 2 = (x-1)/2 ;
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to get:
y = (x-1)/2 ;
or; write as: y = (x/2) - (1/2);
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Now, rewrite; by replacing the "y" with "f⁻¹(x) "; as follows (to indicate that this is the "inverse function"):
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f⁻¹(x) = (x-1)/2 ; or, write as:
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f⁻¹(x) = (x/2) - (1/2) .
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Hope this is helpful to you!
Best wishes!
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