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in Sets, relations and functions by (313 points)

Find the range of f(x) = \(f(x) = log_4 |1 + (1/x)|\)

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1 Answer

+1 vote
by (541 points)

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.smiley

by (313 points)
I have a similar question here!
https://www.sarthaks.com/1836548/find-the-range-of-log-4-x-1-x

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