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

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

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

inverse

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

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

Solution steps

y = 3 \cdot \frac{e}{2} + e^{2 x}

Replace

x

with

y

x = 3 \cdot \frac{e}{2} + e^{2 y}

Solve for

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

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

y = - 3 x^{2} + 100 x + 1

f (x) = 19 x^{2} - 17

f (x) = 8 x - 2 + 5

f (x) = \frac{6}{1 - x}

(21) (21)

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