What is the inverse of f(x)=(5)(2^{(1-x)}) ?

The inverse of f(x)=(5)(2^{(1-x)}) is -(ln(x/5)-ln(2))/(ln(2))

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inverse of f(x)=(5)(2^{(1-x)})

inverse

f (x) = (5) (2^{(1 - x)})

- \frac{ln ( \frac{x}{5} ) - ln ( 2 )}{ln ( 2 )}

Solution steps

y = 5 \cdot 2^{1 - x}

Replace

x

with

y

x = 5 \cdot 2^{1 - y}

Solve for

y, x = 5 2^{1 - y}

- \frac{ln ( \frac{x}{5} ) - ln ( 2 )}{ln ( 2 )}

\frac{3}{2} x + 12

f (x) = \frac{x + 1}{x + 10}

ln (4)

\frac{x}{2} x + 3

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

What is the inverse of f(x)=(5)(2^{(1-x)}) ?
The inverse of f(x)=(5)(2^{(1-x)}) is -(ln(x/5)-ln(2))/(ln(2))