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

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

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inverse of f(x)=sqrt(3-log_{2)(x-1)}

inverse

f (x) = 3 - lo g_{2} (x - 1)

2^{3 - x^{2}} + 1

Solution steps

y = 3 - lo g_{2} (x - 1)

Replace

x

with

y

x = 3 - lo g_{2} (y - 1)

Solve for

y, x = 3 - lo g_{2} (y - 1)

2^{3 - x^{2}} + 1

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

x^{4} - 10 x^{2} + 9

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

f (x) = x^{3} - 6 x^{2} + 1

(8.3) (4.7)

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