What is the inverse of f(x)=log_{3}(9x^2-4) ?

The inverse of f(x)=log_{3}(9x^2-4) is (sqrt(3^x+4))/3 ,-(sqrt(3^x+4))/3

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inverse of f(x)=log_{3}(9x^2-4)

inverse

f (x) = lo g_{3} (9 x^{2} - 4)

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

Solution steps

y = lo g_{3} (9 x^{2} - 4)

Replace

x

with

y

x = lo g_{3} (9 y^{2} - 4)

Solve for

y, x = lo g_{3} (9 y^{2} - 4)

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

f (x) = \frac{3 - 4 x}{8 x - 1}

\frac{x ^{3} + 3 x ^{2} - 4 x}{- 4 x ^{2} + 4 x + 8}

f (x) = \frac{2 ( x ^{2} - 9 )}{x ^{2} - 4}

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

(x + 6) (x - 1)^{2}

What is the inverse of f(x)=log_{3}(9x^2-4) ?
The inverse of f(x)=log_{3}(9x^2-4) is (sqrt(3^x+4))/3 ,-(sqrt(3^x+4))/3