The range of the function f(k) = k2 + 2k + 1 is {25, 64}. what is the function’s domain? a. {5, 8} b. {-5, -8} c. {3, 8} d. {4, 7} e. {4, 8}

Option D

The domain of the function is: {4, 7}

Step-by-step explanation:

We know that for polynomial functions like its domain and its rank are all real numbers. However, for this case we are told that the function range is: the set {25, 64}

This means that the function is bounded.

Then the domain of f(k) are all possible values of k such that f(k) belongs to the interval {25, 64}.

To find the limit values of k then we do f(k) = 25

Now we factor the expression:

Then k = 4 and k = -6.

Now we do f(k) = 64

We factor the expression:

k = -9 and k = 7.

Finally we search between the options given an interval that matches.

The option that matches is option D {4, 7}

D.

Step-by-step explanation:

The given function is

The  domain refers to the value of k, for which the function, is defined.

Observe that the right hand side is a perfect square

We solve for k to get;

when

when

The domain is or

The correct answer is D.

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step-by-step explanation:

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