What is the inverse of f(x)=5+3e^{(2x)} ?

The inverse of f(x)=5+3e^{(2x)} is (ln((x-5)/3))/(2)

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inverse of f(x)=5+3e^{(2x)}

inverse

f (x) = 5 + 3 e^{(2 x)}

\frac{ln ( \frac{x - 5}{3} )}{2}

Solution steps

y = 5 + 3 e^{2 x}

Replace

x

with

y

x = 5 + 3 e^{2 y}

Solve for

y, x = 5 + 3 e^{2 y}

\frac{ln ( \frac{x - 5}{3} )}{2}

f (x) = 3 x^{3} - 13

f (x) = 4 x^{2} + 6 x - 12

f (x) = 3 x - \frac{7}{8}

f (x) = f (x) = ln (x - 1) - ln (2 x + 1)

+ cos (3 θ)

What is the inverse of f(x)=5+3e^{(2x)} ?
The inverse of f(x)=5+3e^{(2x)} is (ln((x-5)/3))/(2)