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

The inverse of f(x)=3log_{2}(x+1)-3 is 2^{(x+3)/3}-1

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inverse of f(x)=3log_{2}(x+1)-3

inverse

f (x) = 3 lo g_{2} (x + 1) - 3

2^{\frac{x + 3}{3}} - 1

Solution steps

y = 3 lo g_{2} (x + 1) - 3

Replace

x

with

y

x = 3 lo g_{2} (y + 1) - 3

Solve for

y, x = 3 lo g_{2} (y + 1) - 3

2^{\frac{x + 3}{3}} - 1

- 3 x^{2} - 12 x + 15

f (x) = \frac{x + 1}{x ^{2} - 2 x - 3}

y = x - 2 + 5

f (x) = \frac{5 x ^{2} + 47 x + 18}{3 x + 27}

f (x) = 5 x^{3} + 8

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