What is the inverse of f(x)=sqrt(log_{3)((x+6)/2)}+1 ?

The inverse of f(x)=sqrt(log_{3)((x+6)/2)}+1 is 3^{x^2-2x+1}*2-6

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inverse of f(x)=sqrt(log_{3)((x+6)/2)}+1

inverse

f (x) = lo g_{3} (\frac{x + 6}{2}) + 1

3^{x^{2} - 2 x + 1} \cdot 2 - 6

Solution steps

y = lo g_{3} (\frac{x + 6}{2}) + 1

Replace

x

with

y

x = lo g_{3} (\frac{y + 6}{2}) + 1

Solve for

y, x = lo g_{3} (\frac{y + 6}{2}) + 1

3^{x^{2} - 2 x + 1} \cdot 2 - 6

y = \frac{1}{2} (1 + e^{x})

- ln (x + 2) + 1

f (x) = \frac{4 x}{3} + \frac{1}{2}

f (x) = 5 ln (1 + 8 x^{3})

f (x) = \frac{5}{6} x - 1

What is the inverse of f(x)=sqrt(log_{3)((x+6)/2)}+1 ?
The inverse of f(x)=sqrt(log_{3)((x+6)/2)}+1 is 3^{x^2-2x+1}*2-6