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Answer:
[tex] {f}^{ - 1} (x) = \frac{1}{4} x[/tex] (last/fourth option)
Step-by-step explanation:
[tex]f(x) = 4x[/tex]
[tex]y = 4x[/tex]
[tex]x = 4y[/tex]
[tex]4y = x[/tex]
[tex] \boxed{\green{{f}^{ - 1} (x) = \frac{1}{4} x}}[/tex]