What is the inverse of f(x)=3-log_{10}(1+x^2) ?

The inverse of f(x)=3-log_{10}(1+x^2) is sqrt(10^{3-x)-1},-sqrt(10^{3-x)-1}

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inverse of f(x)=3-log_{10}(1+x^2)

inverse

f (x) = 3 - lo g_{10} (1 + x^{2})

1 0^{3 - x} - 1, - 1 0^{3 - x} - 1

Solution steps

y = 3 - lo g_{10} (1 + x^{2})

Replace

x

with

y

x = 3 - lo g_{10} (1 + y^{2})

Solve for

y, x = 3 - lo g_{10} (1 + y^{2})

1 0^{3 - x} - 1, - 1 0^{3 - x} - 1

What is the inverse of f(x)=3-log_{10}(1+x^2) ?
The inverse of f(x)=3-log_{10}(1+x^2) is sqrt(10^{3-x)-1},-sqrt(10^{3-x)-1}