Question

If F(x) = log 4 3x, find F -1(x). A.4^y=3x B.4^x=3y C.4^3y=x

Answer 1

Answer:

${f}^{ - 1} (x) = \frac{{4}^{x} }{3}$

Step-by-step explanation:

The given logarithmic function is

$f(x) = log_{4}(3x)$

Let y=f(x)

This gives us:

$y = log_{4}(3x)$

We interchange x and y to get:

$x = log_{4}(3y)$

${4}^{x} = 3y$

$y = \frac{{4}^{x} }{3}$

Therefore the inverse is

${f}^{ - 1} (x) = \frac{{4}^{x} }{3}$

Based on the possible answers, B is most closed to the inverse.

The correct answer is B