- #1
spartas
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find the inverse function of
f(x)=ln(x-1), x>1
f(x)=ln(x-1), x>1
spartas said:find the inverse function of
f(x)=ln(x-1), x>1
The inverse function of f(x) = ln(x-1) is f^-1(x) = e^x + 1.
To find the inverse of f(x) = ln(x-1), switch the x and y variables and solve for y. In this case, it would be x = ln(y-1). Then, rewrite the equation in exponential form to get y = e^x + 1, which is the inverse function.
The domain of f(x) = ln(x-1) is all real numbers greater than 1, since the natural logarithm of 0 or a negative number is undefined. The range is all real numbers.
Yes, the inverse of f(x) = ln(x-1) is a one-to-one function because each input has a unique output and vice versa. This can be seen by graphing both functions and observing that they are reflections of each other across the line y = x.
Yes, the inverse of f(x) = ln(x-1) can also be written as f^-1(x) = log(e, x+1), where log(e, x) represents the natural logarithm with base e. These two forms are equivalent and can be used interchangeably.