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Use the figure to solve the inequality.

f(x) < g(x)

Answer Choices
a. {x|x ≤ -1 or x ≥ 3}; (-∞, -1] or [3, ∞)
b. {x|-1 ≤ x ≤ 3}; [-1, 3]
c. {x|-1 < x < 3}; (-1, 3)
d. {x|x < -1 or x > 3}; (-∞, -1) or (3, ∞)

Use the figure to solve the inequality fx lt gx Answer Choices a xx 1 or x 3 1 or 3 b x1 x 3 1 3 c x1 lt x lt 3 1 3 d xx lt 1 or x gt 3 1 or 3 class=


Answer :

semsee45

Answer:

d. {x | x < -1 or x > 3}; (-∞, -1) or (3, ∞)

Step-by-step explanation:

To solve the inequality of f(x) < g(x), we need to find the intervals where the graph of f(x) lies below the graph of g(x) on the coordinate plane.

From observation of the provided graph, the points of intersection of the two functions are (-1, 3) and (3, -5), indicating that at these points f(x) = g(x).

Now we need to assess the position of f(x) relative to g(x) on either side of the points of intersection:

  • When x < -1, the graph of f(x) lies below the graph of g(x).
  • When -1 < x < 3, the graph of f(x) lies above the graph of g(x).
  • When x > 3, the graph of f(x) lies below the graph of g(x).

As we are looking for the intervals where f(x) lies below g(x), the solution to the inequality f(x) < g(x) is x < -1 or x > 3.

In set-builder notation, the solution is expressed as {x | x < -1 or x > 3}.

In interval notation, the solution is expressed as (-∞, -1) ∪ (3, ∞).

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