What is the inverse of f(x)=4^x+2^{x+1}+3 ?

The inverse of f(x)=4^x+2^{x+1}+3 is (ln(-1+sqrt(x-2)))/(ln(2)),(ln(-sqrt(x-2)-1))/(ln(2))

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inverse of f(x)=4^x+2^{x+1}+3

inverse

f (x) = 4^{x} + 2^{x + 1} + 3

\frac{ln ( - 1 + x - 2 )}{ln ( 2 )}, \frac{ln ( - x - 2 - 1 )}{ln ( 2 )}

Solution steps

y = 4^{x} + 2^{x + 1} + 3

Replace

x

with

y

x = 4^{y} + 2^{y + 1} + 3

Solve for

y, x = 4^{y} + 2^{y + 1} + 3

\frac{ln ( - 1 + x - 2 )}{ln ( 2 )}, \frac{ln ( - x - 2 - 1 )}{ln ( 2 )}

f (x) = 4 x^{2} - 25

f (x) = ln (5 x + 3)

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

f (x) = \frac{x}{25}

f (x) = \frac{4 x + 3}{7}

What is the inverse of f(x)=4^x+2^{x+1}+3 ?
The inverse of f(x)=4^x+2^{x+1}+3 is (ln(-1+sqrt(x-2)))/(ln(2)),(ln(-sqrt(x-2)-1))/(ln(2))