What is the inverse of f(x)=log_{1/2}(x/4) ?

The inverse of f(x)=log_{1/2}(x/4) is (1/2)^x*4

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inverse of f(x)=log_{1/2}(x/4)

inverse

f (x) = lo g_{\frac{1}{2}} (\frac{x}{4})

(\frac{1}{2})^{x} \cdot 4

Solution steps

y = lo g_{\frac{1}{2}} (\frac{x}{4})

Replace

x

with

y

x = lo g_{\frac{1}{2}} (\frac{y}{4})

Solve for

y, x = lo g_{\frac{1}{2}} (\frac{y}{4})

(\frac{1}{2})^{x} \cdot 4

x - 2

- 2 cos (3 x)

f (x) = 2 x^{2} - 8 x + 3

\frac{9}{x}

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

What is the inverse of f(x)=log_{1/2}(x/4) ?
The inverse of f(x)=log_{1/2}(x/4) is (1/2)^x*4