What is the inverse of f(x)=(3sqrt(x)-5)/2 ?

The inverse of f(x)=(3sqrt(x)-5)/2 is (4x^2)/9+(20x)/9+25/9

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inverse of f(x)=(3sqrt(x)-5)/2

inverse

f (x) = \frac{3 x - 5}{2}

\frac{4 x ^{2}}{9} + \frac{20 x}{9} + \frac{25}{9}

Solution steps

y = \frac{3 x - 5}{2}

Replace

x

with

y

x = \frac{3 y - 5}{2}

Solve for

y, x = \frac{3 y - 5}{2}

\frac{4 x ^{2}}{9} + \frac{20 x}{9} + \frac{25}{9}

y = \frac{( 7 x - 2 )}{( 4 x + 5 )}

f (x) = \frac{5}{( x + 3 )}

f (x) = - 2 x - 4

y = (x - 3)^{2} + 2

What is the inverse of f(x)=(3sqrt(x)-5)/2 ?
The inverse of f(x)=(3sqrt(x)-5)/2 is (4x^2)/9+(20x)/9+25/9