What is the inverse of f(x)=log_{2}((e^x-6)/4) ?

The inverse of f(x)=log_{2}((e^x-6)/4) is ln(2^{x+2}+6)

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inverse of f(x)=log_{2}((e^x-6)/4)

inverse

f (x) = lo g_{2} (\frac{e ^{x} - 6}{4})

ln (2^{x + 2} + 6)

Solution steps

y = lo g_{2} (\frac{e ^{x} - 6}{4})

Replace

x

with

y

x = lo g_{2} (\frac{e ^{y} - 6}{4})

Solve for

y, x = lo g_{2} (\frac{e ^{y} - 6}{4})

ln (2^{x + 2} + 6)

(- 2, - 8), (2, - 3)

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

(y - 3)^{2} = 8 (x - 5)

f (x) = \frac{x ^{2} + 6 x + 9}{x ^{3} + 7 x ^{2}}

f (x) = x^{3} + 6 x^{2} + 8 x

What is the inverse of f(x)=log_{2}((e^x-6)/4) ?
The inverse of f(x)=log_{2}((e^x-6)/4) is ln(2^{x+2}+6)