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

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

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

inverse

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

\frac{3 e ^{\frac{4 x - 3}{5}} + 1}{12}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{3 e ^{\frac{4 x - 3}{5}} + 1}{12}

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