The inverse function is written as [tex]f^{-1}(x)[/tex] =x³+15x²+75x+125 and the inverse is a function.
The inverse of a function is defined as the opposite function . Ideally we use a function to map the dependent variable y based on the independent variable x. Inverse function is the relation which defines the value of x depending on a particular value of y.
For an inverse function the domain of the function changes to the range and vice-versa.
Mathematically for a function defined as y=g(x) where g(x) is a polynomial of x . We solve the equation for x in terms of y.
Given function is g(x)=∛x-5
Therefore it can be written as
y= ∛x-5
or, y+5=∛x
Cubing both sides we get:
(y+5)³=(∛x)³
or, y³+15y²+75y+125=x
or, x=y³+15y²+75y+125
So the inverse function can be written as:
[tex]f^{-1}(x)[/tex]=x³+15x²+75x+125 and the inverse function exists.
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