Question

Help
g(x) = 4 + x + e^x; Find inverse of g(5) or g^-1(5)

I got:
y = 4 + x + e^x
x = 4 + y + e ^y
x - 4 = y + e^y
and...What do I do with the e^y?

Thank you.

Answer 1

finding g^-1 (5) means to put g(x)= 5 and finding the value of x.
so, 5= 4 + x + e^x
can u find one obvious solution to this ?

Answer 2

really? is that how it is? I tohught you have to ge the inverse first then substitute 5

Answer 3

thats the simpler way out..

Answer 4

you could take ln to both sides. This will make "e" disappear and the exponent with be brought down as a coefficient. ln e = 1

Answer 5

so..
x - 4 = y + e^y
ln x - ln 4 = ln y + y
log (base e) x - log (base e) 4 = log(base e) y + y..

...how would i isolate y?

andharnm...how would it work out if i followed your suit. would it still give me the same answer as the long method?

Answer 6

hartnn*

Answer 7

@hartnn

Answer 8

u cannot isolate y by taking log,
all u can do is guess one of the obvious solution as x=0
verify it.

Answer 9

I couldn't think of a way either. hopefully someone else will come along

Answer 10

...so..
5 = 4 + x + e^x
5 = 4 + (0) + (e)^0
5 = 4 + 0 + 1
5 = 5
so...what does that tell me...
that there is a solution somewhere along the way?

Answer 11

this tells you that g^-1 (5) = 0
and since g is a function., g^-1 (5) has a unique solution and in this case that unique solution is 0

Answer 12

ok..so the answe r is 0 then?

Answer 13

yup.

Answer 14

ok ill try

Answer 15

hahahahaha!! you're right! Cool!!! Thanks.

Answer 16

welcome :)