find the inverse of the function f(x)=4x^2+1

Question

i need an answer

Answer 1

Interchange variables, i.e. x = 4y² + 1.

 

Solve for the y!  Relabel it as the inverse of f!

 

In this instance, the quadratic function f does not have an inverse that is also a function, for two reasons:

(1) when you attempt to solve for the new y, you have to take square root and put ± in front of that expression, so for some x, you get TWO y values,

(2) original graph fails the HORIZONTAL LINE TEST, which is necessary for f to have an inverse that is also a function.