Question

3. Which is the inverse of the function f(x) = 4x^2?

Answer 1

Answer:

$f^{-1}(x)=\frac{\sqrt{x}}{4}$

Step-by-step explanation:

The inverse of the function is the "opposite" of a function, so to speak. One can find it by treating it like a literal equation with 2 variables, one now has to solve for the other variable presnet. In other words, treat the therm (f(x)) like another variable in the equation. Now one has to solve for (x) in terms of (f(x)).

$f(x)=4x^{2}$

Manipulate the literal equation with inverse operations;

$f(x)=4x^{2}\\\sqrt{}\\\\\\\sqrt{f(x)}=4x\\/4\\\\\frac{\sqrt{f(x)}}{4}=x$

Now switch the variables;

$f^{-1}(x)=\frac{\sqrt{x}}{4}$

The $f^{-1}(x)$ signifies that the written function is the inverse of the original function.