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

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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]}

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