Is General Anaesthesia Advisable For A Person With High Resting Rate Of Heart?

I am hoping to undergo a cosmetic surgery procedure and the plastic surgeon would like to use general anesthesia. I have a fast resting heart rate (usually in the high 80s or low 90s) but I m very slender, I run for 30 minutes each day, never smoked rarely drink. I ve had a relatively high resting heart rate for as long as I can remember I m not really sure why. I also have been taking my blood pressure lately and it seems to fall in the normal/prehypertension category mostly. I am just wondering if general anesthesia is safe, as I was told it can have an affect on heart rate and blood pressure. Thank you.