Answer
f^-1(x) =√[(3-x)÷3]
Explanation:
y=-3x^2+3
interchange 'y' with 'x'
x=-3y^2+3
make y the subject
3y^2=3-x
divide by '3' both sides
y^2=(3-x)÷3
apply square root both sides
√(y^2)=√[(3-x)÷3]
y=√[(3-x)÷3]
f^-1(x) =√[(3-x)÷3]
the inverse of the given function is
f^-1(x)=√[(3-x)÷3]