Respuesta :
It’s been a while but I’m pretty sure you swap the variables. So for simplicity in my steps I’m replacing f(x) with y. So you start with y=cube root of x+12
First you need to swap variables so the equation is now x= cube root of y+12
Then you need to remove the cube root by cubing each side which gives you x^3= y+12
Then subtract 12 from both sides giving you x cubed - 12 =y
Finally you must replace the y with f^-1 (x) to show it’s an inverse so the inverse is f^-1 (x) = x cubed - 12 or if you’re using y, it would be y= x cubed - 12
First you need to swap variables so the equation is now x= cube root of y+12
Then you need to remove the cube root by cubing each side which gives you x^3= y+12
Then subtract 12 from both sides giving you x cubed - 12 =y
Finally you must replace the y with f^-1 (x) to show it’s an inverse so the inverse is f^-1 (x) = x cubed - 12 or if you’re using y, it would be y= x cubed - 12
Answer:
[tex]x^{3} -12[/tex]
Step-by-step explanation:
[tex]y=\sqrt[3]{x+12}[/tex]
Replace x with y to get
[tex]x=\sqrt[3]{y+12}[/tex]
Cube both side
[tex]x^{3}=y+12[/tex]
Subract 12 from both sides
[tex]x^3-12=y[/tex]
