The inverse of y=4 x²+5 is y = √((x-5)/4).
Inverse functions are those that cancel one another out. In other words, if g(x) is f's inverse, then f(g(x)) = g(f(x)) = x. (x). Given an equation for which we want the inverse, we have a fantastic method we can utilize to do this.
Not every function has a counterpart. If f(x) has an inverse, it is clear to see that it will never again have the same value. We give this resource a special name.
A function (f(x)) is said to be one-to-one if each member of the range corresponds to exactly one element of the domain.
Given,
We have a function,
y=4 x²+5
subtracting 5 from each side.
⇒ y - 5 = 4 x²
Divide by 4 and then either
⇒ x² = (y - 5) / 4
⇒ x = √((y-5)/4)
Just change the labels now, x to y.
⇒ y = √((x-5)/4)
So, the inverse of given function is y = √((x-5)/4)
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