What is the inverse of f(x)=4x^2-5 ?

The inverse of f(x)=4x^2-5 is (sqrt(x+5))/2 ,-(sqrt(x+5))/2

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inverse of f(x)=4x^2-5

inverse

f (x) = 4 x^{2} - 5

\frac{x + 5}{2}, - \frac{x + 5}{2}

Solution steps

y = 4 x^{2} - 5

Replace

x

with

y

x = 4 y^{2} - 5

Solve for

y, x = 4 y^{2} - 5

\frac{x + 5}{2}, - \frac{x + 5}{2}

f (x) = - 4^{x + 5}

y = - \frac{3}{4} x - \frac{3}{2}

f (x) = 2 (x - 3)^{2} + 4

4 x + 20 y = - 180

x - 5

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