Video Transcript
Find the domain of the function 𝑓
of 𝑥 equals the negative cube root of two 𝑥 plus 10.
We recall that the domain of a
function is the set of all possible values of 𝑥 such that 𝑓 of 𝑥 is defined. We have been given a cube root
function, which unlike a square root function imposes no restrictions on the
domain. The following is a sketch of the
main cubed root function. We note that the function extends
to the left and the right side of the 𝑦-axis, indicating that the cube root can
take any real number.
This brings to mind a theorem
regarding the domain of the cubed root function, which states that the domain of 𝑓
of 𝑥 equals the cubed root of 𝑥 is the set of all real numbers. The domain may also be written as
the open interval from negative ∞ to positive ∞.
Next, we take a look at the
expression under the cubed root. This expression is of the form 𝑎𝑥
plus 𝑏, meaning it is linear. This linear function adds no
restrictions to the possible values of 𝑥. Therefore, the domain of the
function 𝑓 of 𝑥 equals the negative cube root of two 𝑥 plus 10 is the set of real
numbers.
