1. **Problem:** Evaluate the function $f(x)=2x+1$ at several inputs. 2. **Formula used:** For any input $x$, substitute it into $f(x)=2x+1$ and simplify. 3. **Important rule:** When evaluating a function, replace the variable with the given value first, then do the arithmetic carefully. 4. **a. Find $f(1)$** $$f(1)=2(1)+1$$ $$f(1)=2+1=3$$ 5. **b. Find $f(-2)$** $$f(-2)=2(-2)+1$$ $$f(-2)=-4+1=-3$$ 6. **c. Find $f\left(\frac{1}{2}\right)$** $$f\left(\frac{1}{2}\right)=2\left(\frac{1}{2}\right)+1$$ $$f\left(\frac{1}{2}\right)=1+1=2$$ 7. **d. Find $f(a)$** $$f(a)=2a+1$$ 8. **e. Find $f(a-b)$** $$f(a-b)=2(a-b)+1$$ $$f(a-b)=2a-2b+1$$ 9. **Final answers:** $f(1)=3$, $f(-2)=-3$, $f\left(\frac{1}{2}\right)=2$, $f(a)=2a+1$, and $f(a-b)=2a-2b+1$.