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

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

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inverse of f(x)= 1/2 log_{3}(x)+3/2

inverse

f (x) = \frac{1}{2} lo g_{3} (x) + \frac{3}{2}

3^{2 x - 3}

Solution steps

y = \frac{1}{2} lo g_{3} (x) + \frac{3}{2}

Replace

x

with

y

x = \frac{1}{2} lo g_{3} (y) + \frac{3}{2}

Solve for

y, x = \frac{1}{2} lo g_{3} (y) + \frac{3}{2}

3^{2 x - 3}

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

\frac{x - 1}{1 + 4 x}

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

f (x) = (x - 1)^{3} - 3

f (x) = \frac{6}{8 + x}

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