Question

If g(x) = 9 + x + e^x, find g−1(10).

Answer 1

g-1= inverse of g(x)

Answer 2

ok so first i get x=9+y+e^y

Answer 3

then lnx=ln9+lny+y

Answer 4

Im not sure if this is the correct method because I am unsure what to do next

Answer 5

you are thinking way to hard

Answer 6

you don't need to find the inverse function

Answer 7

\[g^{-1}(10)=x \\ g(x)=10\]
just look for an x such that 9+x+e^(x) will give you 10

Answer 8

also taking ln( ) of both sides would not give you ln(x)=ln(9)+ln(y)+y
it would give you ln(x)=ln(9+y+e^y)

Answer 9

But anyways on this questions you are not actually expected to find the inverse function

Answer 10

just the value

Answer 11

ah i see thanks!

Answer 12

ok so how do I solve for x from x+e^x=1

Answer 13

you don't solve

Answer 14

you think of a number x that will make 9+x+e^x , 10

Answer 15

oh so 0

Answer 16

yes

Answer 17

thank u!

Answer 18

\[9+0+e^0=9+0+1=10 \\ g(0)=10 => g^{-1}(10)=0\]

Answer 19

np