What is the inverse of f(x)=3^{2x+1}-4 ?

The inverse of f(x)=3^{2x+1}-4 is (ln(x+4)-ln(3))/(2ln(3))

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inverse of f(x)=3^{2x+1}-4

inverse

f (x) = 3^{2 x + 1} - 4

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

Solution steps

y = 3^{2 x + 1} - 4

Replace

x

with

y

x = 3^{2 y + 1} - 4

Solve for

y, x = 3^{2 y + 1} - 4

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

x - 11

f (x) = 60 - 4.9 x^{2}

\frac{1}{x ^{2} + 1}

12 x + 4

12 x + 5

What is the inverse of f(x)=3^{2x+1}-4 ?
The inverse of f(x)=3^{2x+1}-4 is (ln(x+4)-ln(3))/(2ln(3))