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If function F is defined by f(x) = 3x^2 + 5, what is f(x-4)

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Answer:

The function f(x) when x=x-4 is
f(x-4)=3x^2-24x+53 or
f(x-4)=3x(x-8)+53

Explanation:

Given function f is defined by
f(x)=3x^2+5

Now to find the function f(x-4):


f(x)=3x^2+5

Put x=x-4 in the above function we get


f(x-4)=3(x-4)^2+5


f(x-4)=3(x^2-2(x)(4)+4^2)+5 (using the formula
(a-b)^2=a^2-2ab+b^2)


f(x-4)=3(x^2-8x+16)+5


f(x-4)=3x^2-24x+48+5 (adding the like terms)


f(x-4)=3x^2-24x+53


f(x-4)=3x(x-8)+53

Therefore
f(x-4)=3x^2-24x+53 or
f(x-4)=3x(x-8)+53

The function f(x) when x=x-4 is
f(x-4)=3x^2-24x+53 or
f(x-4)=3x(x-8)+53

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