The range of the function f(k) = k2 + 2k + 1 is {25, 64}. What is the function’s domain?

Question

i dont know how to explain this please help me!!!!

Answer 1

The range of the given function is a discrete set, i.e. there are just two possible outputs from the function (25, and 64). The question is what numbers can be put into the function "machine" that will generate that output?

Let's determine the input that will generate an output of 25.

Note that k²+2k+1 can be written at (k+1)², i.e. a perfect square trinomial can be written as a binomial squared.

(k+1)²=25

k+1 = ±5 (square root property)

k=±5-1

k = 4 or k = -6

Now do the same to determine the numbers that generate an output of 64.

k+1 = ±8

k = ±8-1

k = 7 or k = -9

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