Problem

Compare the values of two functions at \(x=3\): \(f(x)=2x+1\) and \(g(x)=10\).

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What this problem is really about

A fair function-value comparison holds the input fixed and lets only the outputs differ. We’ll substitute the requested input into each rule, respecting multiplication before addition and recognizing when a function’s output is constant. Then the two evaluated numbers can be compared directly, with no need to compare the formulas’ appearances.

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Substituting x=3 gives f(3)=7 and g(3)=10, so f has the greater value.

Substituting x=3 gives f(3)=2+3+1=6 and g(3)=10, so g has the greater value.

Substituting x=3 gives f(3)=7 and g(3)=30, so g has the greater value.

Substituting x=3 gives f(3)=2(3)+1=7 and g(3)=10, so g has the greater value.

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Compare the values of two functions at \(x=3\): \(f(x)=2x+1\) and \(g(x)=10\).

What this problem is really about

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