What is the inverse of f(x)=log_{5}(sqrt(x-2))+1 ?

The inverse of f(x)=log_{5}(sqrt(x-2))+1 is 25^{x-1}+2

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inverse of f(x)=log_{5}(sqrt(x-2))+1

inverse

f (x) = lo g_{5} (x - 2) + 1

2 5^{x - 1} + 2

Solution steps

y = lo g_{5} (x - 2) + 1

Replace

x

with

y

x = lo g_{5} (y - 2) + 1

Solve for

y, x = lo g_{5} (y - 2) + 1

2 5^{x - 1} + 2

+ ln (x^{2} - 4)

\frac{2 x + 4}{3}

f (x) = \frac{( x + 6 )}{( x - 7 )}

f (x) = \frac{2}{2}

f (x) = \frac{3 x + 4}{2 - x}

What is the inverse of f(x)=log_{5}(sqrt(x-2))+1 ?
The inverse of f(x)=log_{5}(sqrt(x-2))+1 is 25^{x-1}+2