What is the inverse of f(x)=(x+1/2)^2-9/4 ?

The inverse of f(x)=(x+1/2)^2-9/4 is (sqrt(4x+9)-1)/2 ,(-sqrt(4x+9)-1)/2

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inverse of f(x)=(x+1/2)^2-9/4

inverse

f (x) = (x + \frac{1}{2})^{2} - \frac{9}{4}

\frac{4 x + 9 - 1}{2}, \frac{- 4 x + 9 - 1}{2}

Solution steps

y = (x + \frac{1}{2})^{2} - \frac{9}{4}

Replace

x

with

y

x = (y + \frac{1}{2})^{2} - \frac{9}{4}

Solve for

y, x = (y + \frac{1}{2})^{2} - \frac{9}{4}

\frac{4 x + 9 - 1}{2}, \frac{- 4 x + 9 - 1}{2}

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

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

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

f (x) = 5 x^{\frac{1}{4}}

h (x) = \frac{2 x + 17}{3 x + 1}

What is the inverse of f(x)=(x+1/2)^2-9/4 ?
The inverse of f(x)=(x+1/2)^2-9/4 is (sqrt(4x+9)-1)/2 ,(-sqrt(4x+9)-1)/2