Video Transcript
Which of the following is the
equation 𝑦 cubed equals 𝑥 squared plus one expressed in function notation? Is it (A) 𝑓 of 𝑥 equals 𝑥
squared plus one? (B) 𝑓 of 𝑥 equals 𝑥 squared plus
one all cubed. Is it (C) this cannot be expressed
as a function? (D) 𝑓 of 𝑥 equals the cube root
of 𝑥 squared plus one. Or (E) 𝑓 of 𝑦 is equal to 𝑥
squared plus one.
To write any equation in function
notation, we need to see whether we can express 𝑦 as a function of 𝑥 such that 𝑦
is equal to 𝑓 of 𝑥. We will therefore rearrange the
equation to make 𝑦 the subject. In order to do this, we will cube
root both sides of the equation. This gives us 𝑦 is equal to the
cube root of 𝑥 squared plus one. We observe that 𝑦 is now written
as a function of 𝑥. In other words, to find the value
of 𝑦, we can substitute a value of 𝑥 into the expression the cube root of 𝑥
squared plus one. To express 𝑦 cubed equals 𝑥
squared plus one in function notation, we have 𝑓 of 𝑥 is equal to the cube root of
𝑥 squared plus one. The correct answer is option
(D).
