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

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

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

inverse

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

\frac{9 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{9 x ^{2} - 5}{2}

f (x) = 1 - 3 x

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

f (x) = 2 x^{3} - 3 x^{2} + 9 x - 6

f (x) = x^{2} - 6 x + 8

\frac{3}{x} + 1

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