Question

The function f(x)=(x+4)^2+3 is not one-to-one. Identify a restricted domain that makes the function one-to-one, and find the inverse function.

A. restricted domain: x<= -4; f^-1(x)=-4+ sqrt x-3

B. restricted domain: x>=-4; f^-1 (x)=-4 - sqrt x+3

C. restricted domain: x>= -4; f^-1(x) =-4+ sqrt x-3

D. restricted domain: x<= -4; f^-1(x)= -4+ sqrt x+3

Answer 1

B.

Explanation:

answer B is correct for Plato users!!!!

Answer 2

C.Restricted domain :
`x\geq -4`,
`f^(-1)(x)=-4+√(x-3)`

Explanation:

We are given that a function is not one - to-one.

`f(x)=(x+4)^2+3`

Suppose
`y=(x+4)^2+3`

`y-3=(x+4)^2`

`x+4=√(y-3)`

`x=√(y-3)-4`

Hence,
`f^(-1)(x)=-4+√(x-3)`

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

Substitute x=3 then we get

`f^(-1)(x)=-4`

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

Range of
`f^(-1)(x)=[-4,\infty)`

Domain of f(x)=
`[-4,\infty)`

Restricted domain :
`x\geq -4`

Hence, restricted domain of f(x) that makes the function one-to-one .