What is the inverse of f(x)=ln(5-x)+ln(x-3) ?

The inverse of f(x)=ln(5-x)+ln(x-3) is 4-sqrt(-e^x+1),sqrt(-e^x+1)+4

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inverse of f(x)=ln(5-x)+ln(x-3)

inverse

f (x) = ln (5 - x) + ln (x - 3)

4 - - e^{x} + 1, - e^{x} + 1 + 4

Solution steps

y = ln (5 - x) + ln (x - 3)

Replace

x

with

y

x = ln (5 - y) + ln (y - 3)

Solve for

y, x = ln (5 - y) + ln (y - 3)

4 - - e^{x} + 1, - e^{x} + 1 + 4

What is the inverse of f(x)=ln(5-x)+ln(x-3) ?
The inverse of f(x)=ln(5-x)+ln(x-3) is 4-sqrt(-e^x+1),sqrt(-e^x+1)+4