What is the inverse of f(x)=2log_{4}(4x+1)-6 ?

The inverse of f(x)=2log_{4}(4x+1)-6 is (2^{x+6}-1)/4

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inverse of f(x)=2log_{4}(4x+1)-6

inverse

f (x) = 2 lo g_{4} (4 x + 1) - 6

\frac{2 ^{x + 6} - 1}{4}

Solution steps

y = 2 lo g_{4} (4 x + 1) - 6

Replace

x

with

y

x = 2 lo g_{4} (4 y + 1) - 6

Solve for

y, x = 2 lo g_{4} (4 y + 1) - 6

\frac{2 ^{x + 6} - 1}{4}

y = (\frac{1}{5})^{x}

- 3 x + 8

f (x) = 8 + 4 x - 2

\frac{x}{5 + x}

- e^{- x}

What is the inverse of f(x)=2log_{4}(4x+1)-6 ?
The inverse of f(x)=2log_{4}(4x+1)-6 is (2^{x+6}-1)/4