Question

find the inverse of f(x) = sqrt(4-e^2x)

Answer 1

multiplicative inverse?

Answer 2

1/sqrt(4-e^2x)

Answer 3

thats not right

Answer 4

solve it for x=...
let f(x) = y
then:
y^2=4-e^2x
2x=ln|4-y^2|
x=1/2 ln|4-y^2|

now write inverse function as:
f=1/2 ln|4-x^2|

Answer 5

is it good?

Answer 6

i dont understand the answer

Answer 7

inverse function is 1/2 on natural ln of absolute value (...):
\[f=1/2 \ln|4-x ^{2}|\]

Answer 8

after y^2=4-e^2x

I am LOST!

Answer 9

how do you finish solving for x

Answer 10

e^2x=4-y^2
take ln both sides:
2x=ln|4-y^2|
x=...

because it's inverse - just change places for x& y

Answer 11

ok i understand now

Answer 12

so what will be the domain of the inverse function

Answer 13

\[4-x^{2}>0\]
because ln

Answer 14

\[x^{2}<4\]
-2<x<2

Answer 15

-2 doesnt work

Answer 16

that's why (-2) & 2 are not included.
it simple more & less (not equal)