What is the inverse of f(x)=3log_{5}(x+1)-2 ?

The inverse of f(x)=3log_{5}(x+1)-2 is 5^{(x+2)/3}-1

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inverse of f(x)=3log_{5}(x+1)-2

inverse

f (x) = 3 lo g_{5} (x + 1) - 2

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

Solution steps

y = 3 lo g_{5} (x + 1) - 2

Replace

x

with

y

x = 3 lo g_{5} (y + 1) - 2

Solve for

y, x = 3 lo g_{5} (y + 1) - 2

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

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

x^{3} - 6 x^{2}

f (x) = 4 x^{2} + 7

\frac{3 - x}{x - 2}

y = \frac{1}{2} x + 2

What is the inverse of f(x)=3log_{5}(x+1)-2 ?
The inverse of f(x)=3log_{5}(x+1)-2 is 5^{(x+2)/3}-1