What is the inverse of f(x)=-3log_{10}(1/2 (x-2))-5 ?

The inverse of f(x)=-3log_{10}(1/2 (x-2))-5 is 5^{-(x+5)/3}*2^{1-(x+5)/3}+2

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inverse of f(x)=-3log_{10}(1/2 (x-2))-5

inverse

f (x) = - 3 lo g_{10} (\frac{1}{2} (x - 2)) - 5

5^{- \frac{x + 5}{3}} \cdot 2^{1 - \frac{x + 5}{3}} + 2

Solution steps

y = - 3 lo g_{10} (\frac{1}{2} (x - 2)) - 5

Replace

x

with

y

x = - 3 lo g_{10} (\frac{1}{2} (y - 2)) - 5

Solve for

y, x = - 3 lo g_{10} (\frac{1}{2} (y - 2)) - 5

5^{- \frac{x + 5}{3}} \cdot 2^{1 - \frac{x + 5}{3}} + 2

f (x) = x + 2, x \geq - 2

e^{6} x - 13 x - 3

\frac{4 x - 1}{x}

f (x) = \frac{1}{1 + a \cdot x}

cos (\frac{0}{12})

What is the inverse of f(x)=-3log_{10}(1/2 (x-2))-5 ?
The inverse of f(x)=-3log_{10}(1/2 (x-2))-5 is 5^{-(x+5)/3}*2^{1-(x+5)/3}+2