Step-by-step explanation:
y=f (x) then x= g (y)
x=3y
solve x=3y for y
if f(x) = g(x),then in(f(x)).
in(x)= yin(3)
y= in(x) / in(3)
The inverse function of the given function is [tex]y=\dfrac{\ln x}{\ln 3}[/tex].
Important information:
Interchange [tex]x[/tex] and [tex]y[/tex].
[tex]x=3^y[/tex]
Taking ln on both sides, we get
[tex]\ln x=\ln 3^y[/tex]
[tex]\ln x=y\ln 3[/tex]
[tex]\dfrac{\ln x}{\ln 3}=y[/tex]
Therefore, the inverse function of the given function is [tex]y=\dfrac{\ln x}{\ln 3}[/tex].
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