find the inverse of the following function. Find the domain, range,and asymptotes of each function. Graph both functions on the same coordinate plane.
f(x)=3+lnx
y = 3 + lnx
first step in finding the inverse is to interchange the x and y variables, so
inverse is
x = 3 + lny
x-3 = lny
y = e^(x-3)
in original y = 3 + lnx
domain , x > 0 , y is any real number
so in the inverse these two would be interchanged.
remember , when graphing an inverse of a function, you get a reflection in the line y = x
check:
in original, let x = 5
y = 3+ln5 = 4.6094... (I stored it in memory)
in inverse:
x = 4.6094
y = e^(1.6094) = 5
Yeahh