HELLO,
As per question we have to find the range of \(f(x) = \log_4(1+\frac{1}{x})\)
Let \(f(x) =y
\)
Now,
\(y=\log_4(1+\frac{1}{x})\)
For finding range we have to make a equation like this \(x=f(y)
\) and then find the domain of \(f(y)
\) which is actually range of \(f(x)
\)
\(4^y = 1+\frac{1}{x}\)
\(4^y-1 = \frac{1}{x}\)
\(x=\frac{1}{4^y-1}\)
Here, domain of y is \(y\in R-\{0\}\) because at only 0 f(x) is not defined.
RANGE OF \(f(x) =R-\{0\}\)
I HOPE YOU WILL UNDERSTAND.