f(x)=(1e^x-12)/(17e^x+9)
F(x^-1)=?
the domain F(x^-1) is open and interval(a, b)
where a=? and b=?
F(x^-1)=?
the domain F(x^-1) is open and interval(a, b)
where a=? and b=?
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Find the inverse by inverting the variables and solving for the new "y"
x=(e^y-12)/(17e^y+9)
x(17e^y+9)=e^y-12
17e^y x + 9x = e^y -12
17e^y x - e^y = -9x -12
e^y(17x-1) = -9x -12
e^y = (-9x-12)/(17x-1)
y = ln [(-9x-12)/(17x-1)]
Remembering that the natural domain of ln(x) is (0,infinity),
then [(-9x-12)/(17x-1)]>0 which implies that -4/3
x=(e^y-12)/(17e^y+9)
x(17e^y+9)=e^y-12
17e^y x + 9x = e^y -12
17e^y x - e^y = -9x -12
e^y(17x-1) = -9x -12
e^y = (-9x-12)/(17x-1)
y = ln [(-9x-12)/(17x-1)]
Remembering that the natural domain of ln(x) is (0,infinity),
then [(-9x-12)/(17x-1)]>0 which implies that -4/3
1
keywords: function,Inverse,points,10,of,Inverse of a function... 10 points!