### Video Transcript

Find the domain of the function 𝑓
of 𝑥 equals the square root of seven 𝑥 minus seven.

We have here a composite square
root function. If we allow 𝑔 of 𝑥 to be the
function under the square root, so 𝑔 of 𝑥 is equal to seven 𝑥 minus seven, then
𝑓 of 𝑥 is equal to the square root of 𝑔 of 𝑥. We recall that the domain of a
composite square root function of the form 𝑓 of 𝑥 equals the square root of 𝑔 of
𝑥 can be found by finding the set of all values of 𝑥 such that 𝑔 of 𝑥 is
nonnegative. We therefore need to solve the
inequality seven 𝑥 minus seven is greater than or equal to zero.

We can do this by first adding
seven to each side, giving seven 𝑥 is greater than or equal to seven. And then we can divide each side of
the inequality by seven to give 𝑥 is greater than or equal to one. We can express this in interval
notation as the left-closed, right-open interval from one to ∞.