Question

i(x)=1−3×10^(2x+3)

I have the range and domain as being x all the reals and y less than one but I don't understand why
I have started doing the inverse of the function but I am stuck and the person who was helping me has gone offline :(

Answer 1

HI!!

Answer 2

you don't know why \[1-3\times 10^{2x+3}<1\]?

Answer 3

\[10^{2x+3}\] is positive, so \[-3\times 10^{2x+3}\] is negative

Answer 4

that makes the whole thing always less that one

Answer 5

ahhhh ok :)

Answer 6

Are you able to help with the inverse?

Answer 7

sure why not?

Answer 8

\[1-3\times 10^{2x+3}=y\\
-3\times 10^{2x+3}=y-1\\
10^{2x+3}=\frac{1-y}{3}\\
2x+3=\log(\frac{1-y}{3})\]

Answer 9

then you solve for \(x\)
\[2x=\log(\frac{1-y}{3})-3\\
x=\frac{1}{2}\log(\frac{1-y}{3})-\frac{3}{2}\]

Answer 10

Awwww thank you so very much

Answer 11

\[\color\magenta\heartsuit\]

Answer 12

can I ask does this function have asymptotes?