The answer is: 7/5 ; or write as: 1⅖ ; or write as 1.4 .
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Explanation:
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Given: f(x) = 5x − 10; Find f⁻¹(-3).
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→ Find: f ⁻¹(x) = 5x − 10 ;
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→ Write: f(x) = 5x − 10; as:
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→ y = 5x − 10 ;
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→ Replace the "x" with the "y", and the 'y" with the "x"; and Rewrite:
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→ x = 5y − 10 ;
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Now, rewrite the ABOVE equation in "slope-intercept form"; or "y = mx + b"; that is: with "y" as a "stand-alone" variable on the left-hand side;
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We have: x = 5y − 10 ;
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Subtract "x" ; and subtract "5y" ; from EACH side of the equation:
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→ x − x − 5y = 5y − 10 − x − 5y ;
→ -5y = -10 − x ; Multiply the ENTIRE EQUATION (both sides) by "-1" ;
→ -1* {-5y = -10 − x} ;
→ 5y = 10 + x ; ↔ 5y = x + 10 ;
→ Now, divide EACH side of the equation by "5" ;
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→ 5y / 5= (x + 10) /5 ;
→ y = x/5 + 10/5 ;
→ y = x/5 + 2 ; Now we can replace "y" with: f⁻¹(x) ;
→ f⁻¹(x) = x/5 + 2
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Now, to find: f⁻¹(-3) ; we plug "3" for "x" in this [inverse] function:
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→ f⁻¹(-3) = (-3)/5 + 2 = -⅗ + 2 = 7/5 ; or write as: 1⅖ ; or write as 1.4 .
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