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!
Algebra.Com
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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