What is the inverse of f(x)=1+1/2 e^{3t+2} ?

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

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inverse of f(x)=1+1/2 e^{3t+2}

inverse

f (x) = 1 + \frac{1}{2} e^{3 t + 2}

\frac{ln ( 2 t - 2 ) - 2}{3}

Solution steps

x = 1 + \frac{1}{2} e^{3 t + 2}

Replace

t

with

x

t = 1 + \frac{1}{2} e^{3 x + 2}

Solve for

x, t = 1 + \frac{1}{2} e^{3 x + 2}

\frac{ln ( 2 t - 2 ) - 2}{3}

f (x) = 10 e^{2 x}

f (x) = - 2 sin (x + \frac{π}{3}) + 2

f (x) = 49 + 2.2 (x - 61)

2 x - 9

\frac{2 ^{x} + 8}{3 - 2 ^{x}}

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