What is the inverse of f(x)= 1/2 log_{10}(4x) ?

The inverse of f(x)= 1/2 log_{10}(4x) is 25^x*2^{2x-2}

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inverse of f(x)= 1/2 log_{10}(4x)

inverse

f (x) = \frac{1}{2} lo g_{10} (4 x)

2 5^{x} \cdot 2^{2 x - 2}

Solution steps

y = \frac{1}{2} lo g_{10} (4 x)

Replace

x

with

y

x = \frac{1}{2} lo g_{10} (4 y)

Solve for

y, x = \frac{1}{2} lo g_{10} (4 y)

2 5^{x} \cdot 2^{2 x - 2}

\frac{x - 2}{3}

6 + 2 x - 2

f (x) = 2 - 3 x^{2}, x \leq 0

f (x) = 4 (7)^{x}

What is the inverse of f(x)= 1/2 log_{10}(4x) ?
The inverse of f(x)= 1/2 log_{10}(4x) is 25^x*2^{2x-2}