When substituting value for variables must I always surround the variables with parenthesis? I also mean to include this for functions where for example if I had:
- f(x) = 3x+5 and I say evaluate at f(3). Would I evaluate as 3(3)+5 or would I evaluate as 3*3+5. They mean the same thing but does it matter in some situations where negatives are involved?
As you pointed out, it does mean the same thing in that situation. However, it is good practice to make sure the correct order of operations happens. This in turn will help your calculator understand you better.
For the usual real numbers, you can use $*$ like you said, and it will mean the same thing. Things look a little stranger with negatives, as in $3*-1$, but I can still read and understand that. However, other times that might not work out!
For example, when distributive property might need to happen... $$f(x+1)=3(x+1)+5=3x+3+5=3x+8$$ Then without parenthesis it may seem that $$f(x+1)=3*x+1+5=3x+6.$$
Also remember that the calculator reads $-3^2$ and $(-3)^2$ as different things!
So, in conclusion, I'd say it's a good habit to put the parentheses, but they are not always necessary.