K(x) = x^2(x^2 + 16), where K(x) = x^2.
I got K(x^2) = x^8 + 16x^4. Is this right? Thanks :))
Whoops, I meant we had to find the value of the function K(x^2), not where K(x)=x^2. Sorry about that lol
If K(x) = x^2(x^2 + 16) then
K(x^2) = x^4(x^4 + 16)
= x^8 + 16x^4
you are right.
but...
your first line is confusing.
either K(x) = x^2(x^2 + 16) or K(x) = x^2
ok, saw your correction
To find K(x^2), you need to substitute x^2 into the expression for K(x). Let's do that step by step:
Step 1: Start with the given expression for K(x): K(x) = x^2(x^2 + 16)
Step 2: Replace every occurrence of "x" with "x^2": K(x^2) = (x^2)^2((x^2)^2 + 16)
Step 3: Simplify the exponents inside the parentheses: K(x^2) = x^4(x^4 + 16)
Step 4: Distribute x^4 to the terms inside the parentheses: K(x^2) = x^4 * x^4 + x^4 * 16
Step 5: Simplify each term: K(x^2) = x^8 + 16x^4
So, your answer is correct! K(x^2) = x^8 + 16x^4. Well done!