Question

Which statement best describes f(x)=-2sqrt(x-7+1)


A.-6 is in the domain of f(x) but not in the range of f(x)

B.-6 is not the domain of f(x) but is in the range of of f(x)

C.-6 is in the domain of f(x) and in the range of f(x)

D. -6 is neither in the domain of f(x) nor in the range of f(x)

Answer 1

Plugging -6 in for x, we get -2sqrt(-6-7+1)=sqrt(something negative) which is clearly not possible.

Plugging -6 in for f(x), we get -6=-2sqrt(x-7+1) and 3=sqrt(x-7+1). Squaring both sides, we get 9=x-7+1 and by adding both sides by 6 we get 15=x, therefore having (15,-6) and proving that -6 is in the range, but not the domain (B)

Answer 2

The statement which best describes the function is that the -6 is neither in the domain of f(x) nor in the range of f(x). Option D is correct.

What is domain and range of function?

Domain of a function is the set of all the possible input values which are valid for that function.

Range of a function is the set of all the possible output values which are valid for that function.

The function of x is given as,

$f(x)=-2\sqrt{(x-7+1)}$

Simplify the function further,

$f(x)=-2\sqrt{(x-7+1)}\\f(x)=-2\sqrt{(x-6)}$

The domain of this function is [6,∞) and the range is from (∞,0].

Hence, the statement which best describes the function is that the -6 is neither in the domain of f(x) nor in the range of f(x). Option D is correct.

Learn more about the domain and range of the function here;

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