What is the inverse of f(x)=-2^{x+1}+4 ?

The inverse of f(x)=-2^{x+1}+4 is (ln(4-x))/(ln(2))-1

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inverse of f(x)=-2^{x+1}+4

inverse

f (x) = - 2^{x + 1} + 4

\frac{ln ( 4 - x )}{ln ( 2 )} - 1

Solution steps

y = - 2^{x + 1} + 4

Replace

x

with

y

x = - 2^{y + 1} + 4

Solve for

y, x = - 2^{y + 1} + 4

\frac{ln ( 4 - x )}{ln ( 2 )} - 1

f (x) = 4 x - \frac{7}{8}

f (x) = ln (x^{2} + 2 x + 2)

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

f (x) = \frac{7}{6 x + 1}

What is the inverse of f(x)=-2^{x+1}+4 ?
The inverse of f(x)=-2^{x+1}+4 is (ln(4-x))/(ln(2))-1