Answer:
[tex]f^{-1}(x)=\frac{1}{2}\sqrt{x}[/tex]
Step-by-step explanation:
To find the inverse of a function, change the f(x) to a y, switch the places of x and y, then solve for the new y:
[tex]f(x)=4x^2[/tex] becomes [tex]y=4x^2[/tex]
Now switch the places of x and y:
[tex]x=4y^2[/tex] and solve for the new y:
[tex]\frac{1}{4}x=y^2[/tex]
Take the square root of both sides to "undo" the square on the y:
[tex]\sqrt{\frac{1}{4}x } =y[/tex]
and the square root of 1/4 is 1/2, so we have in the end:
[tex]y=\frac{1}{2}\sqrt{x}[/tex]
Now you can put it back into inverse function notation since that is, after all, an inverse function:
[tex]f^{-1}(x)=\frac{1}{2}\sqrt{x}[/tex]
