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

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SUMMARY

The discussion centers on the functions ƒ(x) as a linear function and g(x) as a rational function, with specific values provided for both functions at x = 3 and x = 4. The claim is that there exists a solution to the equation ƒ(x) = g(x) between x = 3 and x = 4, which must be closer to 3 than to 4. The consensus is that while a solution exists in the interval, it is not guaranteed to be closer to 3, thus making the statement FALSE.

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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.

Can you post what you have done so far?
 
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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