what is the inverse operation of raising a number to the 4th power, and how can it be used to find the…

what is the inverse operation of raising a number to the 4th power, and how can it be used to find the inverse of the function ( f(x)=x^{4}-1 )? choose the correct answer below.\na. the inverse operation of raising a number to the 4th power is taking the 4th root of a number. to find the inverse of ( f(x) ), take the 4th root of both sides to undo the 4th power and then add 1 to both sides. the result is the inverse of ( f(x) ).\nb. the inverse operation of raising a number to the 4th power is taking the 4th root of a number. to find the inverse of ( f(x) ), add 1 to both sides and then take the 4th root of both sides to undo the 4th power. the result is the inverse of ( f(x) ).\nc. the inverse operation of raising a number to the 4th power is dividing a number by 4. to find the inverse of ( f(x) ), divide both sides by 4 to undo the 4th power and then add 1 to both sides. the result is the inverse of ( f(x) ).\nd. the inverse operation of raising a number to the 4th power is dividing a number by 4. to find the inverse of ( f(x) ), add 1 to both sides and then divide by 4 to undo the 4th power. the result is the inverse of ( f(x) ).
Answer
Explanation:
Step1: Solve for (x) in (y = x^{4}-1)
Let (y = f(x)=x^{4}-1). To find the inverse, we first swap (x) and (y): (x = y^{4}-1).
Step2: Isolate (y^{4})
Add (1) to both sides: (x + 1=y^{4}).
Step3: Take the 4th root
Take the 4th root of both sides: (y=\sqrt[4]{x + 1}). The inverse operation of raising a number to the 4th power is taking the 4th root.
Answer:
B. The inverse operation of raising a number to the 4th power is taking the 4th root of a number. To find the inverse of (f(x)), add (1) to both sides and then take the 4th root of both sides to undo the 4th power. The result is the inverse of (f(x))