What is the inverse of f(x)=(3^x+2)^2+4 ?

The inverse of f(x)=(3^x+2)^2+4 is (ln(sqrt(x-4)-2))/(ln(3)),(ln(-sqrt(x-4)-2))/(ln(3))

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inverse of f(x)=(3^x+2)^2+4

inverse

f (x) = (3^{x} + 2)^{2} + 4

\frac{ln ( x - 4 - 2 )}{ln ( 3 )}, \frac{ln ( - x - 4 - 2 )}{ln ( 3 )}

Solution steps

y = (3^{x} + 2)^{2} + 4

Replace

x

with

y

x = (3^{y} + 2)^{2} + 4

Solve for

y, x = (3^{y} + 2)^{2} + 4

\frac{ln ( x - 4 - 2 )}{ln ( 3 )}, \frac{ln ( - x - 4 - 2 )}{ln ( 3 )}

f (x) = (5 x^{3} - 1) + 7

\frac{2}{s ^{2} + 6 s + 8}

f (x) = - \frac{1}{3 x}

f (x) = \frac{( 2 x + 1 )}{( x - 3 )}

What is the inverse of f(x)=(3^x+2)^2+4 ?
The inverse of f(x)=(3^x+2)^2+4 is (ln(sqrt(x-4)-2))/(ln(3)),(ln(-sqrt(x-4)-2))/(ln(3))