The inverse of function f( x ) = ( 2x - 3)² is [tex]y=\frac{\pm\sqrt{x} +3}{2}[/tex].
A function that can reverse into another function is known as an inverse function or anti-function. A function takes in values, applies specific operations to them, and produces an output. In order to find y when x is swapped with another variable, we must first determine the inverse function. On the other hand, the inverse function and the original function likewise have interchangeable domains and ranges.
We have the function,
f(x) = y = ( 2x - 3 )²
x = ( 2y - 3 )²
2y - 3 = ±√x
Adding 3 from each side.
2y - 3 + 3 = ±√x + 3
2y = ±√x + 3
Dividing each side of the equation by 2.
[tex]y=\frac{\pm\sqrt{x} +3}{2}[/tex]
Hence, the inverse of function f( x ) = ( 2x - 3 )² is [tex]y=\frac{\pm\sqrt{x} +3}{2}[/tex].
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