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VLD [36.1K]
3 years ago
13

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

Mathematics
2 answers:
Svetach [21]3 years ago
7 0

Answer:

Hence, the domain of the function is:

{4,7}

Step-by-step 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}

Lady_Fox [76]3 years ago
6 0
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}
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