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Let f(x)=2x+3 and let g(x)=x^(2)-4x. Which of the following is equivalent to g(f(x)) ? Choose 1 answer: (A) 4x^(2)+4x-3 (B) 4x^(2)-8x-3 (c) 4x^(2)+4x+21 (D) 2x^(2)-8x+3

Let f(x)=2x+3 f(x)=2 x+3 and let g(x)=x2−4x g(x)=x^{2}-4 x . Which of the following is equivalent to g(f(x)) g(f(x)) ?\newlineChoose 11 answer:\newline(A) 4x2+4x−3 4 x^{2}+4 x-3 \newline(B) 4x2−8x−3 4 x^{2}-8 x-3 \newline(C) 4x2+4x+21 4 x^{2}+4 x+21 \newline(D) 2x2−8x+3 2 x^{2}-8 x+3

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Full solution

Q. Let f(x)=2x+3 f(x)=2 x+3 and let g(x)=x2−4x g(x)=x^{2}-4 x . Which of the following is equivalent to g(f(x)) g(f(x)) ?\newlineChoose 11 answer:\newline(A) 4x2+4x−3 4 x^{2}+4 x-3 \newline(B) 4x2−8x−3 4 x^{2}-8 x-3 \newline(C) 4x2+4x+21 4 x^{2}+4 x+21 \newline(D) 2x2−8x+3 2 x^{2}-8 x+3
  1. Substitute f(x)f(x) into g(x)g(x): First, substitute f(x)f(x) into g(x)g(x) to get g(f(x))g(f(x)).\newlineg(f(x))=g(2x+3)g(f(x)) = g(2x+3)
  2. Plug in 2x+32x+3: Now, plug in 2x+32x+3 wherever there's an xx in g(x)g(x).\newlineg(2x+3)=(2x+3)2−4(2x+3)g(2x+3) = (2x+3)^2 - 4(2x+3)
  3. Expand and distribute: Expand the square and distribute the −4-4.g(2x+3)=(2x+3)(2x+3)−8x−12g(2x+3) = (2x+3)(2x+3) - 8x - 12
  4. Multiply out the terms: Multiply out the terms.\newlineg(2x+3)=4x2+6x+6x+9−8x−12g(2x+3) = 4x^2 + 6x + 6x + 9 - 8x - 12
  5. Combine like terms: Combine like terms.\newlineg(2x+3)=4x2+12x−8x+9−12g(2x+3) = 4x^2 + 12x - 8x + 9 - 12
  6. Finish combining: Finish combining like terms.\newlineg(2x+3)=4x2+4x−3g(2x+3) = 4x^2 + 4x - 3

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