Question

Consider the function f(x)=x+9−−−−−√−3f(x)=x+9−3 on the domain [−9,[infinity])[−9,[infinity]). The inverse of this function is f−1(x)=x2+6xf−1(x)=x2+6x. A: What is the domain of f−1f−1? B: Why must the domain of f−1f−1 be restricted?

Answer 1

Answer with Step-by-step explanation:

We are given that a function
`f(x)=√(x+9)-3`

Domain of f(x)=[-9,
`\infty`)

The inverse of given function
`f^(-1)(x)=x^2+6x`

a.We have to find the domain of
`f^(-1)(x)`

We know that domain of f(x) is convert into range of
`f^(-1)(x)` and range of f(x) is convert into domain of
`f^(-1)(x)`

If we substitute x=-9 in the given function then we get

`f(x)=√(-9+9)-3=-3`

Therefore, range of f(x) =[-3,
`\infty`)

Domain of
`f^(-1)(x)=[-3,[tex]\infty)`

b.Range of f(x) is restricted .Therefore, domain of
`f^(-1)(x)` must be restricted because range of f(x) is converted into domain of
`f^(-1)(x)` and range of f(x) is restricted.