Which of these functions has an inverse function? Select all that apply.y = xy = x^2y = x^3y = x^4

ANSWERy=xy=x³ EXPLANATIONA function, f(x) has an inverse if and only if [tex]f(a) = f(b) \Rightarrow \: a = b[/tex]Thus, the function is one to one.For y=x or[tex]f(x) = x[/tex][tex]f(a) = f(b) \Rightarrow \: a = b[/tex]Hence this function has an inverse.For the function y=x² or f(x)=x².[tex]f(a) = f(b) \Rightarrow \: {a}^{2} = {b}^{2} \Rightarrow \: a = \pm \: b[/tex]This function has no inverse on the entire real numbers.For the function y=x³ or f(x)=x³[tex]f(a) = f(b) \Rightarrow \: {a}^{3} = {b}^{3} \Rightarrow \: a = b[/tex]This function also has an inverse.For y=x⁴ or f(x) =x⁴ [tex]f(a) = f(b) \Rightarrow \: {a}^{4} = {b}^{4} \Rightarrow \: a = \pm \: b[/tex]This function has no inverse over the entire real numbers.