Answer: " f ⁻¹ (x) = [tex] \frac{x}{4} [/tex] " .
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Explanation:
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"Find the inverse of " f(x) = 4x " .
1) Let " f(x) = y = 4x " ;
2) Interchange the "y" and the x" :
→ x = 4y ;
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3) Isolate "y" on one side of the equation:
x = 4y ;
↔ 4y = x ;
Divide each side of the equation by "4" ;
to isolate "y" on each side of the equation:
→ 4y / 4 = x / 4 ;
→ y = x / 4 ;
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Now, change the " y" to: " f ⁻¹ (x) " ; and rewrite:
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→ " f ⁻¹ (x) = [tex] \frac{x}{4} [/tex] " .
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This is our answer. Note that the "f ⁻¹ (x) " denotes the "inverse function".
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