f(x-4)=x^2-8x+7 find f(x)?

f(x) = x^2 - 9

f(x-4) = x^2 -8x + 7 = (x-4)^2 -16+7 = (x-4)^2 - 9. Then f(x) = x^2 - 9.

Let y = x - 4

f (y) = (y + 4)² - 8(y + 4) + 7

f (y) = y² + 8y + 16 - 8y - 25

f (y) = y² - 9

f (x) = x² - 9

f(x-4) = x^2-8x+7
Let y=x-4
x = y+4
f(y) = (y+4)^2 -8(y+4) + 7
f(y) = y^2+8y+16-8y-32+7
f(y) = y^2-9
f(x) = (x-4)^2 - 9
f(x) = x^2-8x+16-9
f(x) = x^2-8x+7

x-4=x'--> x'=x+4
f (x')=(x'+4)^2-8 (x'+4)+7=
=x'^2+8x'+16-8x'-32+7
=x'^2-9
f (x) = x^2-9
f (x-4) = x^2-8x+16-9=x^2-8x+7

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