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

Solution:

Given:

f(k)=k²+2k+1

Range = {25, 64}

To find the domain of the given function

Consider for k = x range is 25

x² + 2x + 1 = 25

x² + 2x - 24 = 0

By splitting up of the middle term

x² + 6x - 4x - 24 = 0

Taking out the common terms

x (x + 6) - 4 (x + 6) = 0

(x + 6) (x - 4) = 0

So we get

x = {4, -6}

Consider for k = y range is 64

x² + 2x + 1 = 64

x² + 2x - 63 = 0

By splitting up of the middle term

x² + 9x - 7x - 63 = 0

Taking out the common terms

x (x + 9) - 6 (x + 9) = 0

(x + 9) (x - 6) = 0

So we get

x = {6, -9}

Therefore, the domain is D € {-9 , -6, 4, 6}.

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

Summary:

The range of the function f(k)=k²+2k+1 is {25, 64}. The function domain is D € {-9 , -6, 4, 6}.