Answer:
[tex]{f}^{ - 1} (x) = \frac{{4}^{x} }{3} [/tex]
Step-by-step explanation:
The given logarithmic function is
[tex]f(x) = log_{4}(3x) [/tex]
Let y=f(x)
This gives us:
[tex]y = log_{4}(3x) [/tex]
We interchange x and y to get:
[tex]x = log_{4}(3y) [/tex]
[tex] {4}^{x} = 3y[/tex]
[tex]y = \frac{{4}^{x} }{3} [/tex]
Therefore the inverse is
[tex] {f}^{ - 1} (x) = \frac{{4}^{x} }{3} [/tex]
Based on the possible answers, B is most closed to the inverse.
The correct answer is B
