Question

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

{5, 8}
{-5, -8}
{3, 8}
{4, 7}
{4, 8}

Answer 1

The domain of a function contains the x-values of the function while the range of the function contains the y-values of the function. In this case, we substitute 25 and 64 to y. Then,
25 = k2 + 2 k + 1 (k-4) * (k+6) = 0
64 = k2 + 2 k + 1 (k-7) * (k+9) = 0
hence the domain is {-9,-6, 4,7}

Answer 2

Hence, the domain of the function is:

{4,7}

Explanation:

We are given the range of the function:

`f(k)=k^2+2k+1` as {25,16}

The function f(k) could also be written as:

`f(k)=k^2+2k+1=k^2+k+k+1\\\\f(k)=k(k+1)+1(k+1)\\\\f(k)=(k+1)(k+1)\\\\f(k)=(k+1)^2`

The range is the value of the function at some k.

1)

if f(k)=25 then we have to find the value of k.

`f(k)=25=5^2=(k+1)^2`

on taking square root on both side we have:

`k+1=5\\\\k=5-1\\\\k=4`

2)

if f(k)=64 then we have to find the value of k.

`f(k)=64=8^2=(k+1)^2`

on taking square root on both side we have:

`k+1=8\\\\k=8-1\\\\k=7`

Hence, the domain of the function is:

{4,7}