suppose we have following function

$f(x)={x}^{2}+10\mathrm{sin}(x)$

we should show that there exist number $c$ such that $f(c)=1000$

clearly we can solve this problem using intermediate value theorem for instance

$f(0)=0$

$f(90)={90}^{2}+10\mathrm{sin}(90)=8100+10\ast 1=8110$

and because 1000 is between these two number we can see that there exist such c so that $f(c)=1000$

am i right? thanks in advance

$f(x)={x}^{2}+10\mathrm{sin}(x)$

we should show that there exist number $c$ such that $f(c)=1000$

clearly we can solve this problem using intermediate value theorem for instance

$f(0)=0$

$f(90)={90}^{2}+10\mathrm{sin}(90)=8100+10\ast 1=8110$

and because 1000 is between these two number we can see that there exist such c so that $f(c)=1000$

am i right? thanks in advance