James Chen TMUA Paper 1 · Question 13

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James Chen TMUA Paper 1 · Q13

Paper 1Logic & proofFunctions & graphs

The real numbers $a,b$ are such that $a>b$ . You are given that the function $f(x)$ is defined over positive real $x$ and is either always increasing or always decreasing. Which of these conditions is sufficient but not necessary for $f(a)<f(b)$ to be true?

f'(x)<0

f(x)

is a decreasing function

f(x)=\log_c x

0<c<1

f(x)=\log_c x

c>1

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