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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = - \frac{1}{( 4 t - 7 ) ^{2}}

\frac{2 s + 1}{3 s ^{2} + 27}

f (x) = 0.95905

3 + 7 - 3 x^{2}

y = x^{2} - 1

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