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hpfan101
 one year ago
Find a formula for the inverse of the function.
f(x)=(4x1)/(2x+3)
y=ln(x+3)
y=x^2  x
y=(1+e^x)/(1+e^x)
hpfan101
 one year ago
Find a formula for the inverse of the function. f(x)=(4x1)/(2x+3) y=ln(x+3) y=x^2  x y=(1+e^x)/(1+e^x)

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freckles
 one year ago
Best ResponseYou've already chosen the best response.4if the function is onetoone, you just solve the equation for x

freckles
 one year ago
Best ResponseYou've already chosen the best response.4\[y=\frac{ax+b}{cx+d} \\ \text{ multiply both sides by } cx+d \\ (cx+d)y=ax+b \\ \text{ distribute on the left } \\ cx y +dy=ax+b \\ \text{ now remember you want to solve for } x \\ \text{ get all of your terms with } x \text{ on one side } \\ \\ \text{ so subtract } ax \text{ and } dy \text{ on both sides } \\ cxyax=bdy \\ \text{ now this allows you to do the following so you can solve for } x \\ x(cya)=bdy \\ \text{ now divide both sides by } (cya)\]

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.0Oh, ok. Thank you! :)

freckles
 one year ago
Best ResponseYou've already chosen the best response.4after solving for x,interchange x any y

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.0y=(1+e^x)/(1+e^x) How about the very last one? The negative exponent is confusing me.

freckles
 one year ago
Best ResponseYou've already chosen the best response.4if the negative exponent confused you can multiply top and bottom by e^x

freckles
 one year ago
Best ResponseYou've already chosen the best response.4\[y=\frac{1+e^{x}}{1+e^{x}} \cdot \frac{e^{x}}{e^{x}} \\ y=\frac{e^{x}+1}{e^{x}+1}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.4lol (1+exp(x))/(1+exp(x)) is 1

freckles
 one year ago
Best ResponseYou've already chosen the best response.4\[y=\frac{1+e^{x}}{1+e^{x}}=1 \]

freckles
 one year ago
Best ResponseYou've already chosen the best response.4and f(x)=1 is not onetoone

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.0I think the typo is that the numerator is (1e^x) while the denominator is (1+e^x). But would that make that much of a difference?

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.0Oh wait, it would. You can't simplify it to be 1.

freckles
 one year ago
Best ResponseYou've already chosen the best response.4yes! now the top is different from the bottom the function is not 1 anymore now verify the function is onetoone and if it is solve for e^x and then solve for x and if is not you are done because no inverse function exist

freckles
 one year ago
Best ResponseYou've already chosen the best response.4I said solve for e^x because you can still multiply top and bottom by e^x giving you \[f(x)=\frac{e^{x}1}{e^{x}+1}\]

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.0Ah I see how to solve it now. Thanks again!

freckles
 one year ago
Best ResponseYou've already chosen the best response.4are you looking for inverse relation or function?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4so did you verify f(x)=(1exp(x))/(1+exp(x)) is onetoone? you can use a graphing calculator and see if it passes the horizontal line test?

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.0Oh ok. So I plugged it into the graphing calculator and the function doesn't pass he horizontal line test.

hpfan101
 one year ago
Best ResponseYou've already chosen the best response.0Actually, it does. Nevermind, it looked like it didn't at first.

freckles
 one year ago
Best ResponseYou've already chosen the best response.4ok so that means you have to actually solve that equation above for e^x then x
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