Let ๐โก(๐ฅ)= 2โข๐ฅ2. Find and simplify the following:(a) ๐โข(๐ฅ+3)= ย (b) ๐โก(๐ฅ+3)-๐โก(3)=
Question
Let . Find and simplify the following:
(a)
(b)
Solution
Sure, let's solve this step by step:
(a) ๐โก(๐ฅ+3)=
We substitute x+3 into the function f(x) = 2x^2:
f(x+3) = 2*(x+3)^2 = 2*(x^2 + 6x + 9) = 2x^2 + 12x + 18
So, f(x+3) = 2x^2 + 12x + 18
(b) ๐โก(๐ฅ+3)-๐โก(3)=
We already know f(x+3) from part (a), so we just need to find f(3) and subtract it:
f(3) = 2*(3)^2 = 2*9 = 18
Now, subtract f(3) from f(x+3):
f(x+3) - f(3) = (2x^2 + 12x + 18) - 18 = 2x^2 + 12x
So, f(x+3) - f(3) = 2x^2 + 12x
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