Find the Inverse

Question

Find the inverse of the function f(x)=2(3^(x-2))-1

Answer 1

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

Step 1) replace f(x) with "y":

y = 2(3^(x-2)) - 1

Step 2) switch the "x" and "y":

x = 2(3^(y-2)) - 1

Step 3) solve for "y":

x = 2(3^(y-2)) - 1

x + 1 = 2(3^(y-2))

(x + 1)/2 = 3^(y-2)

log₃[(x + 1)/2] = y - 2

y = log₃[(x + 1)/2] + 2

Step 4) replace "y" with f^-1(x):

f^-1(x) = log₃[(x + 1)/2] + 2