If f(x) = (4/3)ln(7x/5), then f^-1(x) =?

Question

If f(x) = (4/3)ln(7x/5), then f^-1(x) =?

possible solutions....

a. (7/5)e^(4x/3)

b. (7/4)e^(5x/3)

c. (7/4)e^(3x/5)

d. (5/3)e^(7x/4)

e. (5/7)e^(3x/4)

f. (4/5)e^(7x/3)

g. (3/4)e^(5x/7)

h. (3/4)e^(7x/5)

i. (3/7)e^(4x/5)

Answer 1

f(x) = (4/3) ln(7x/5)
To find inverse f
x = (4/3) ln(7 f^-1(x) / 5)
(3/4) x = ln (7 f^-1(x) / 5)
7 f^-1(x) / 5 = e^(3x/4)
f^-1(x) = (5/7)e^(3x/4) (answer e)