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Nonlinear Functions

SAT Math· difficulty 4/5

If g(x)=f(x−3)+2g(x) = f(x-3) + 2 and f(x)=x2f(x) = x^2, what is g(x)g(x) in standard form?

  • A

    x2−6x+11x^2 - 6x + 11

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  • B

    x2+6x+11x^2 + 6x + 11

  • C

    x2−6x+9x^2 - 6x + 9

  • D

    x2−6x+7x^2 - 6x + 7

Explanation

g(x)=(x−3)2+2=x2−6x+9+2=x2−6x+11g(x) = (x-3)^2 + 2 = x^2 - 6x + 9 + 2 = x^2 - 6x + 11.

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