Let $f(x)$ be a continues function for all $x$, and $|f(x)|\le7$ for all $x$.
Prove the equation $2x+f(x)=3$ has one solution.
I think the intermediate value theorem is key in this, but I'm not sure of the proper usage.
Let $f(x)$ be a continues function for all $x$, and $|f(x)|\le7$ for all $x$.
Prove the equation $2x+f(x)=3$ has one solution.
I think the intermediate value theorem is key in this, but I'm not sure of the proper usage.
Hint: Let $g(x)=f(x)+2x-3$. Then $g(-2)$ and $g(5)$ are...