MHB Function - one linear, one rational - is the following True or False

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The discussion centers on whether the statement about the functions ƒ(x) and g(x) is true or false. Given that ƒ(x) is linear and g(x) is rational, the values at x = 3 and x = 4 indicate that there is indeed a point where ƒ(x) equals g(x) between these two values. However, examples exist where the solution could be closer to x = 4 than x = 3. Thus, the assertion that the solution must be closer to 3 is debated. The conclusion is that the statement is false.
bigazonk
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The function ƒ(x) is a linear function and g(x) is a rational function.

These functions have the following values:
ƒ(3) = 7 g(3) = 5.6
ƒ(4) = 5 g(4) = 6.7

There is a solution to the equation ƒ(x) = g(x) between x = 3 and x = 4 that must be closer to 3 than 4.

TRUE or FALSE?
 
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Hello and welcome to MHB, bigazonk! (Wave)

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

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Certainly there exist x in that interval such that f(x)= g(x) but it is easy to find examples in which x is closer to 4 than to 3.
 

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