Find the inverse of f(x) = 2log4 (x - 3)

y = 2 * log[4](x - 3)

Switch x with y, solve for y

x = 2 * log[4](y - 3)
x/2 = log[4](y - 3)
4^(x/2) = y - 3
(2^2)^(x/2) = y - 3
2^(2x / 2) = y - 3
2^x = y - 3
y = 3 + 2^x

To find the inverse, let f(x) = y, interchange x and y, and re-solve for y; the resulting expression in y will be the inverse.

Letting f(x) = y:
y = 2log₄(x - 3).

Interchanging x and y:
x = 2log₄(y - 3).

Then, re-solving for y:
log₄(y - 3) = x/2, by isolating the logarithm function
==> y - 3 = 4^(x/2), by the definition of the logarithm
==> y = f^-1(x) = 4^(x/2) + 3.

I hope this helps!

Assuming that the function is bijective,

Let y=f(x)=2log_4 (x-3)

y/2=log_4 (x-3)

4^(y/2)=x-3

2^(2*y/2)=x-3

2^y=x-3

x=3+2^y

if y=f(x) => x=f^-1(y)

Therefore, f^-1(y)=3+2^y

put y=x

=>f^-1(x)=3+2^x

g(x)=3+2^x is the inverse of f(x).