Question

Find the inverse of f(x)=3e^(x+2/4)-5

Answer 1

first off
\[\frac{2}{4}=\frac{1}{2}\] is there a typo here?

Answer 2

its x+2 over 4

Answer 3

oh wait, i bet it is
\[f(x)=e^{\frac{x+2}{4}}-5\]

Answer 4

bingo

Answer 5

but a 3 in front of e...

Answer 6

ok we write
\[y=3e^{\frac{x+2}{4}}-5\] and solve for x

Answer 7

\[\frac{y}{3}=e^{\frac{x+2}{4}}-5\]
\[\frac{y}{3}+5=e^{\frac{x+2}{4}}\]

Answer 8

do i need to use: e^A=B

Answer 9

\[\frac{x+2}{4}=\ln(\frac{y+15}{3})\]

Answer 10

A=Ln(B)

Answer 11

\[x+2=4\ln(\frac{y+15}{3})\]

Answer 12

\[x=4\ln(\frac{y+15}{3})-2\]

Answer 13

\[f^{-1}(x)=4\ln(\frac{x+15}{3})-2\]

Answer 14

how did you get y+15?

Answer 15

\[\frac{y}{3}+5=\frac{y+15}{3}\] by adding the fractions

Answer 16

d'oh! gotcha. Thanks a million