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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

(x - 3)^{2} + 7

- 2 cos (x)

- lo g_{10} (t)

f (x) = x + 7, x \geq - 7

f (x) = - 5 t^{2} + 10 t + 20, t > 0

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