Answer: f⁻¹ (x) = [tex]\frac{x}{5} [/tex] ;
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→ or; write as: f⁻¹ (x) = [tex] \frac{1}{5} x[/tex] .
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Explanation:
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Given: " f(x) = 5x " ; Find: " f⁻¹ (x) " ;
Note that: " f⁻¹ (x) " is the "inverse function".
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Given: " f(x) = 5x " ;
Rewrite as: " y = 5x" ;
To solve for the "inverse function" ; exchange "x" with "y"; and "y" with "x" ; and rewrite:
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→ x = 5y ;
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Now, isolate "y" on one side of the equation; & solve for "y" ; in terms of "x" ;
→ x = 5y ;
↔ 5y = x ;
Divide EACH SIDE of the equation by "5" ; as follows:
→ 5y / 5 = x / 5 ;
to get:
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→ y = x / 5 ;
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Now, replace the "y" ; with: " f⁻¹ (x) " ;
→ and rewrite; as follows:
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→ f⁻¹ (x) = [tex]\frac{x}{5} [/tex] ;
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→ or, write as:
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→ f⁻¹ (x) = [tex] \frac{1}{5} x[/tex] .
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