SOLUTION: Hello! A function f(x) is given. f(x) = log5(log10(x)) (a) Find the domain of the function f (b) Find the inverse function of f. f -1(x) = thanks for your help!

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Question 198808: Hello!
A function f(x) is given.
f(x) = log5(log10(x))
(a) Find the domain of the function f
(b) Find the inverse function of f.
f -1(x) =
thanks for your help!

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
a)

Since you cannot take the log of 0 or a negative value, this means that and (for the outer and inner logs)


If we solve , we get . So combining the inequalities and (ie perform a set union), we get .

So the domain of is


------------------

b)

Start with the given function.


Replace f(x) with "y"


Switch each x and y


Rewrite the equation using the property: ====>


Rewrite the equation again using the property: ====>


So the inverse function is


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