Question Video: Finding the Domain of Root Functions Mathematics

Find the domain of the function 𝑓(𝑥) = √(7𝑥 − 7).

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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 ∞.