What is the inverse of f(x)=sqrt((7^{x+6))/7} ?

The inverse of f(x)=sqrt((7^{x+6))/7} is (2ln(x))/(ln(7))-5

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inverse of f(x)=sqrt((7^{x+6))/7}

inverse

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

\frac{2 ln ( x )}{ln ( 7 )} - 5

Solution steps

y = \frac{7 ^{x + 6}}{7}

Replace

x

with

y

x = \frac{7 ^{y + 6}}{7}

Solve for

y, x = \frac{7 ^{y + 6}}{7}

\frac{2 ln ( x )}{ln ( 7 )} - 5

10 - 3 - x

y = \frac{2 x - 1}{x + 1}

y = \frac{4}{x ^{2}}

f (x) = \frac{- x - 14}{5}

What is the inverse of f(x)=sqrt((7^{x+6))/7} ?
The inverse of f(x)=sqrt((7^{x+6))/7} is (2ln(x))/(ln(7))-5