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nlexa [21]
2 years ago
6

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 inv

erse 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
Mathematics
2 answers:
zloy xaker [14]2 years ago
8 0

Answer:

C.Restricted domain :x\geq -4, f^{-1}(x)=-4+\sqrt{x-3}

Step-by-step 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=\sqrt{y-3}

x=\sqrt{y-3}-4

Hence, f^{-1}(x)=-4+\sqrt{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 .

lawyer [7]2 years ago
7 0

Answer:

B.

Step-by-step explanation:

answer B is correct for Plato users!!!!

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