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

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

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

inverse

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

\frac{3 x ^{2} - 5}{2}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{3 x ^{2} - 5}{2}

f (x) = \frac{8 - 3 x}{1 - 2 x}

y = 2 x + \frac{5}{2}

f (x) = \frac{( 2 x + 3 )}{x}

g (x) = 2 x + 8

f (x) = \frac{3 x ^{2} + 4}{8}

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