SOLUTION: The one-to-one function g is defined below. g(x)=5x/3x-7 Find g^-1(x), where g^-1 is the inverse of g. Also state the domain and range of g^-1 in interval notation. g^-1(

Question 1037839: The one-to-one function g is defined below.
g(x)=5x/3x-7
Find g^-1(x), where g^-1 is the inverse of g.
Also state the domain and range of g^-1 in interval notation.
g^-1(x) = ?
Domain of g^-1 = ?
Range of g^-1 = ?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The one-to-one function g is defined below.
g(x)=5x/3x-7
Find g^-1(x), where g^-1 is the inverse of g.'
----
y = 5x/(3x-7)
1st:: Interchange x and y::
x = 5y/(3y-7)
2nd:: Solve for "y"::
3xy - 7x = 5y
y(3x-5) = 7x
y = (7x)/(3x-5)
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Also state the domain and range of g^-1 in interval notation.
g^-1(x) = ?
Domain of g^-1 = ?
Vertical asymptote at x = 5/3, so
(-oo,5/3)U(5/3,+oo)
Range of g^-1 = ?
Horizontal asumptote at y = 7/3
(-oo,7/3)U(7/3,+oo)
---------------------
Cheers,
Stan H.
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