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

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

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

inverse

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

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

Solution steps

y = 2^{x} - 2

Replace

x

with

y

x = 2^{y} - 2

Solve for

y, x = 2^{y} - 2

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

f (x) = 100

f (x) = - 5 x^{2} - 9, x \geq 0

f (x) = x^{2} - 16 x + 4

f (x) = \frac{5}{7 x - 8}

f (x) = 0.2 sin (x)

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