let fx 7e4x10 find f14 where f1 is the inverse function of

let f(x) = 7(e^4x)-10. find f^-1(4) where f^-1 is the inverse function of f.

Solution

f(x) = 7(e^4x) - 10

y = 7e^4x - 10

y+10 = 7e^4x

e^4x = (y+10)/7

4x = ln ((y+10)/7)

x = (ln ((y+10)/7)) / 4

y = (ln ((x+10)/7))/4

f^-1(x) =(ln ((x+10)7))/4

f^-1(4) = (ln((4+10)/7))/4

f^-1(4) = (ln(14/7)) / 4

f^-1(4) = (ln 2)/4