What is the inverse of f(x)=5ln(x^2+1)-2 ?

The inverse of f(x)=5ln(x^2+1)-2 is sqrt(e^{(x+2)/5)-1},-sqrt(e^{(x+2)/5)-1}

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inverse of f(x)=5ln(x^2+1)-2

inverse

f (x) = 5 ln (x^{2} + 1) - 2

e^{\frac{x + 2}{5}} - 1, - e^{\frac{x + 2}{5}} - 1

Solution steps

y = 5 ln (x^{2} + 1) - 2

Replace

x

with

y

x = 5 ln (y^{2} + 1) - 2

Solve for

y, x = 5 ln (y^{2} + 1) - 2

e^{\frac{x + 2}{5}} - 1, - e^{\frac{x + 2}{5}} - 1

f (x) = y^{3} + 6

\frac{1}{2 x - 2}

f (x) = - x^{2} + 2 x + 5

f (x) = (x + 4)^{2} - 6

\frac{1}{x ^{6}}

What is the inverse of f(x)=5ln(x^2+1)-2 ?
The inverse of f(x)=5ln(x^2+1)-2 is sqrt(e^{(x+2)/5)-1},-sqrt(e^{(x+2)/5)-1}