Find inverse of  function below. Graph function below and inverse function. Determine domain, range, asymptotes of function and inverse function. f(x) = 7 - In(x + 5)

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f(x)= 7- ln(x+5)

Let y= 7- ln(x+5) 

The domain is all x values such that y is defined.

ln(x+5) is defined when x+5>0 ==> x >-5 

Then the domain is (-5, oo)

 

Now we will find the inverse.

We will switch x and y.

==> x = 7- ln(y+5)

Now we will isolate y.

==> ln (y+5) = 7-x

==> y+5 = e^(7-x)

`==gt y= e^((7-x)) - 5`

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