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

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

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

inverse

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

\frac{ln ( x + 1 )}{ln ( 2 )} - 3

Solution steps

y = 2^{x + 3} - 1

Replace

x

with

y

x = 2^{y + 3} - 1

Solve for

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

\frac{ln ( x + 1 )}{ln ( 2 )} - 3

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

f (x) = \frac{1}{2} lo g_{3} (x) + \frac{3}{2}

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

\frac{x - 1}{1 + 4 x}

f (x) = 2 x - \frac{2}{3}

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