Find the inverse of f(x)=logbase2[logbase3(x+5)] algebraically and state the domain and range of the inverse function.
Can someone give me steps on how to do this problem? I know that you must switch the x and the y and that it would be wise to convert the log to exponential form but I am a bit confused on how to ste this problem up. All help is greatly appreciated.
Can someone give me steps on how to do this problem? I know that you must switch the x and the y and that it would be wise to convert the log to exponential form but I am a bit confused on how to ste this problem up. All help is greatly appreciated.
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Yeah, I'm confused too, but let's try to set it up. We'll use y instead of f(x), then switch x and y at the end (if we get that far) ...
y = log2 [log3 (x + 5)] ==> 2^y = log3 (x + 5) ==> 3^(2^y) = x + 5 ==>
3^(2^y) = (3^2)^y = 9^y = x + 5 ==> x = 9^y - 5
Now switch: y = 9^x - 5 (Answer)
For domain and range, I guess x can be anything, but y will always be positive.
y = log2 [log3 (x + 5)] ==> 2^y = log3 (x + 5) ==> 3^(2^y) = x + 5 ==>
3^(2^y) = (3^2)^y = 9^y = x + 5 ==> x = 9^y - 5
Now switch: y = 9^x - 5 (Answer)
For domain and range, I guess x can be anything, but y will always be positive.