To determine where the function `f(x)=sqrt(7-10x)` is continuous, consider the domain of the square root function. The square root function is defined and continuous wherever its argument is non-negative. Therefore, set up the inequality `7 - 10 x \ge 0` to find the values of `x` for which this holds true. Solve this inequality to determine the range of `x` values that ensure the argument inside the square root remains non-negative.

`(-oo,7/10]`