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

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

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

inverse

f (x) = 2 x - 3

\frac{x ^{2}}{4} + \frac{3 x}{2} + \frac{9}{4}

Solution steps

y = 2 x - 3

Replace

x

with

y

x = 2 y - 3

Solve for

y, x = 2 y - 3

\frac{x ^{2}}{4} + \frac{3 x}{2} + \frac{9}{4}

f (x) = 3 (x - 2)^{2} - 3

\frac{1}{x + 1} + 2

f (x) = \frac{3}{5} - \frac{3}{10} x

f (x) = 2 - 3 x^{2}

f (x) = \frac{x ^{\frac{1}{3}}}{4}

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