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 )}

f (x) = \frac{x + 9}{x - 5}

y = \frac{1}{4} x^{2}

y = \frac{1}{4} x^{3}

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

f (x) = 3 (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))