# Algebra

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Given f(x)=-4+lnx; Find the inverse of f. f^-1=?

• Algebra -

original:
y = 4 + lnx
inverse:
x = 4 + lny
solving for y
lny = x-4
y = e^(x-4)

f^-1 (x) = e^(x-4)

• Algebra -

How do you find the domain and range?

• Algebra -

domain is your choice of x's that you can use in your equation
For logs, one of the main properties is that I can only take the log of a positive number

so for y = 4 + lnx , the domain is x > 0
however, the result of taking such logs results in any real number, so the range is y ∈ R

After taking the inverse of a function, the domain of the original becomes the range of the inverse, and the range of the original becomes the domain of the inverse.

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