The answer is: [C]: " f ⁻¹(x) = (5x + 3) / 2 " .
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Explanation:
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Given: "f(x) = (2x - 3) / 5 ; which is the "inverse" of: " f(x)" ?
Substitute "y" for "f(x)" :
y = (2x - 3) / 5 ;
Replace "x" with "y"; and "y" with "x" ; and rewrite:
x = (2y - 3) / 5 ;
Now, solve for "y" , in term of "x' ;
Multiply each side of the equation by "5"
5 * x = 5 * { (2y - 3) / 5 } ;
to get:
5x = 2y - 3 ;
Add "3" to each side of the equation:
5x + 3 = 2y - 3 + 3 ;
to get: 5x + 3 = 2y ;
↔ 2y = 5x + 3 ;
Divide each side of the question by "2" ;
to isolate "y" on one side of the equation; & to solve for "y" in terms of "x" ;
→ 2y / 2 = (5x + 3) / 2 ;
to get: y = (5x + 3) / 2 ;
Replace the "y" with: " f ⁻¹(x) " ;
and rewrite:
" f ⁻¹(x) = (5x + 3) / 2 " ;
→ which is: "Answer choice: [C]: " f ⁻¹(x) = (5x + 3) / 2 " .
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