What is the inverse of f(x)=log_{2}(3x^2+4) ?

The inverse of f(x)=log_{2}(3x^2+4) is sqrt((2^x-4)/3),-sqrt((2^x-4)/3)

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inverse of f(x)=log_{2}(3x^2+4)

inverse

f (x) = lo g_{2} (3 x^{2} + 4)

\frac{2 ^{x} - 4}{3}, - \frac{2 ^{x} - 4}{3}

Solution steps

y = lo g_{2} (3 x^{2} + 4)

Replace

x

with

y

x = lo g_{2} (3 y^{2} + 4)

Solve for

y, x = lo g_{2} (3 y^{2} + 4)

\frac{2 ^{x} - 4}{3}, - \frac{2 ^{x} - 4}{3}

What is the inverse of f(x)=log_{2}(3x^2+4) ?
The inverse of f(x)=log_{2}(3x^2+4) is sqrt((2^x-4)/3),-sqrt((2^x-4)/3)