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) = 1 + 2 x + 3 x^{2}

f (x) = 12 - 9 x^{3}

f (x) = \frac{1}{3} x - 8

3 - x

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