Find the inverse of the function f(x)=3-e^(x+4)

How do I determine the domain, range, and asymptotes of both the function and the inverse function?

Question

Find the inverse of the function f(x)=3-e^(x+4)

How do I determine the domain, range, and asymptotes of both the function and the inverse function?

campbell_st · Answer

the x = 3 e^(y + 4)

make y the subject

x - 3 = e^(y + 4)

ln(x-3) = y + 4

y = ln(x - 3) - 4

hero · Answer

The domain can only be limited if x is under a square root or in a denominator. Otherwise, it is all real numbers. There are some tricks to finding the range. It involves taking the inverse of the function and switching x and y.

campbell_st · Answer

oops should be y = ln (3 - x) -4

hero · Answer

The domain and range for the function and its inverse are inverses of each other.

hero · Answer

If that makes any sense

anonymous · Answer

so will my domain and range be the same.   i got -inf., 3 as my range