I need to know if.my example for this problem solved

Question

Let $f(x)=\sup(x^3, x^2+1)$, $I=[1,4]$

$\sup(x^3)=64,\ \inf(x^3)=1$

$\sup(x^2+1)=17,\ \inf(x^2+1)=2$

So $\sup(x^3,x^2+1)=\sup(64,17) =64$

Is this correct, can I have good example.

Answer 1

No, you misunderstood the definition of the function $f$: it is the function which, for each $x\in[14]$, takes the value $\sup(x^3,x^2+1)$. For instance

• $f(1)=\sup(1^3,1^2+1)=2$,
• $f(2)=\sup(2^3,2^2+1)=8$,

&c.