For the onetoone function fx 16 x3 2 find the inverse give

For the one-to-one function f(x) = 1/6 x^3 - 2, find the inverse, give the domain and the range for f and f^-1, then What is the domain of f? (Type your answer in interval notation.) What is the range of f? (Type your answer in interval notation.) What is the domain of f^-1? (Type your answer in interval notation.) What is the range of f^-1? (Type your answer in interval notation.)

Solution

f(x) = x^3/6 - 2

Domain : all real ( - inf, inf)

Range : all real ( - inf, inf)

f^-1(x)

y = x^3/6 -2

Plug : x=y and y =x

So, x = y^3/6 - 2

(x+2) = y^3/6

y^3 = 6(x+2)

y = [6(x+2)]^1/3

f^-1(x) =[6(x+2)]^1/3

Domain : all real ( - inf, inf)

Range : all real ( - inf, inf)