What is the inverse of f(x)=-2/3 (2)^{4-3x}+5 ?

The inverse of f(x)=-2/3 (2)^{4-3x}+5 is -(ln(-\frac{3x-15)/(32))}{3ln(2)}

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inverse of f(x)=-2/3 (2)^{4-3x}+5

inverse

f (x) = - \frac{2}{3} (2)^{4 - 3 x} + 5

- \frac{ln ( - \frac{3 x - 15}{32} )}{3 ln ( 2 )}

Solution steps

y = - \frac{2}{3} \cdot 2^{4 - 3 x} + 5

Replace

x

with

y

x = - \frac{2}{3} \cdot 2^{4 - 3 y} + 5

Solve for

y, x = - \frac{2}{3} 2^{4 - 3 y} + 5

- \frac{ln ( - \frac{3 x - 15}{32} )}{3 ln ( 2 )}

\frac{2 x + 1}{5 x - 8}

f (x) = \frac{x ^{3}}{8} + 16

x^{2} - 4

f (x) = \frac{3 + 5 x}{3 - x}

sin (- \frac{1}{2})

What is the inverse of f(x)=-2/3 (2)^{4-3x}+5 ?
The inverse of f(x)=-2/3 (2)^{4-3x}+5 is -(ln(-\frac{3x-15)/(32))}{3ln(2)}