What is the inverse of f(x)=sqrt(2^x-1) ?

The inverse of f(x)=sqrt(2^x-1) is (ln(x^2+1))/(ln(2))

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inverse of f(x)=sqrt(2^x-1)

inverse

f (x) = 2^{x} - 1

\frac{ln ( x ^{2} + 1 )}{ln ( 2 )}

Solution steps

y = 2^{x} - 1

Replace

x

with

y

x = 2^{y} - 1

Solve for

y, x = 2^{y} - 1

\frac{ln ( x ^{2} + 1 )}{ln ( 2 )}

f (x) = 4 - 2^{3 x}

f (x) = 12 - 3 x^{3}

f (x) = (x - 2)

0.3333300000000 \dots x^{2} - 1.4 x + 9.37

f (x) = (- 16 x + 13)^{2}

What is the inverse of f(x)=sqrt(2^x-1) ?
The inverse of f(x)=sqrt(2^x-1) is (ln(x^2+1))/(ln(2))