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The equation of two functions f(x) And g(x) are typed into a graphing calculator to see both graphs on the same coordinate plane. The graphs shown below represents the two functions.

Which are approximate solutions of the equation f(x)=g(x) Select all that apply.

A. 6

B. 0.7

C. 0

D. 4.6

The equation of two functions f x And g x are typed into a graphing calculator to see both graphs on the same coordinate plane

Answer :

The approximate solutions for [tex]\( f(x) = g(x) \)[/tex]based on the graph are [tex]\( x = 0.7 \), \( x = 4.6 \), and \( x = 6 \)[/tex].

The correct option is (A,B and D).

To approximate the solutions of the equation [tex]\( f(x) = g(x) \)[/tex] from the graph, we need to identify the points where the two graphs intersect.

The graph shows two functions, [tex]\( f(x) \) and \( g(x) \)[/tex], and their points of intersection are where[tex]\( f(x) \) equals \( g(x) \)[/tex]. The x-coordinates of these points of intersection are the solutions to the equation [tex]\( f(x) = g(x) \)[/tex].

By observing the graph, we can approximate the points of intersection:

1. The first point of intersection appears to be around ( x = 0.7).

2. The second point of intersection is not visible on the graph.

3. The third point of intersection appears to be around ( x = 4.6 ).

4. The fourth point of intersection is around ( x = 6 ).

From the provided options, the approximate solutions for [tex]\( f(x) = g(x) \)[/tex]based on the graph are [tex]\( x = 0.7 \), \( x = 4.6 \), and \( x = 6 \)[/tex], which correspond to options B, D, and A respectively. Option C, [tex]\( x = 0 \),[/tex] does not seem to be an intersection point on the provided graph.

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Rewritten by : Batagu

Answer:

The solution of the equation f(x) = g(x) is the set of all x for which the graphs of f and g intersect. The solution of the inequality f(x) < g(x) is the set of all x for which the graph of f lies below the graph of g