How do you find the domain and range of #h(x)=ln(x-6)#?

Question

71203 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-02-03T10:16:08

The answers are: #D(6,+oo)# and #R(-oo,+oo)#.

The domain of the function #y=lnf(x)# is: #f(x)>0#.

So:

#x-6>0rArrx>6# or we can write: #D=(6,+oo)#

The range of a function is the domain of the inverse function. The inverse function of the logarithmic function is the exponential function.

So (using the method to find the inverse function, that is: exchange #x# with #y# and finding #y#):

#y=ln(x-6)rArrx=ln(y-6)rArre^x=y-6rArry=e^x+6#,

that has domain #(-oo,+oo)#.

The function is:

graph{ln(x-6) [-2, 15, -5, 5]}