Question

What is f(g(0)))-1 0 1

Answer 1

Let f(x) and g(x) achieve their maximum value at x

1

and x

2

respectively.

h(x)=f(x)−g(x)

h(x

1

)=f(x

1

)−g(x

1

)≥0

h(x

2

)=f(x

2

)−g(x

2

)≤0

⇒h(c)=0 where c∈[0,1] ⇒f(c)=g(c)