What is the inverse of f(x)= 4/3 ln(4x-1/3)-4/5 ?

The inverse of f(x)= 4/3 ln(4x-1/3)-4/5 is (3e^{\frac{15x+12)/(20)}+1}{12}

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inverse of f(x)= 4/3 ln(4x-1/3)-4/5

inverse

f (x) = \frac{4}{3} ln (4 x - \frac{1}{3}) - \frac{4}{5}

\frac{3 e ^{\frac{15 x + 12}{20}} + 1}{12}

Solution steps

y = \frac{4}{3} ln (4 x - \frac{1}{3}) - \frac{4}{5}

Replace

x

with

y

x = \frac{4}{3} ln (4 y - \frac{1}{3}) - \frac{4}{5}

Solve for

y, x = \frac{4}{3} ln (4 y - \frac{1}{3}) - \frac{4}{5}

\frac{3 e ^{\frac{15 x + 12}{20}} + 1}{12}

What is the inverse of f(x)= 4/3 ln(4x-1/3)-4/5 ?
The inverse of f(x)= 4/3 ln(4x-1/3)-4/5 is (3e^{\frac{15x+12)/(20)}+1}{12}