Question Video: Identifying Functions | Nagwa Question Video: Identifying Functions | Nagwa

Question Video: Identifying Functions Mathematics • Second Year of Secondary School

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Which of the following is the equation 𝑦³ = 𝑥² + 1 expressed in function notation? [A] 𝑓(𝑥) = 𝑥² + 1 [B] 𝑓(𝑥) = (𝑥² + 1)³ [C] This cannot be expressed as a function. [D] 𝑓(𝑥) = ∛(𝑥² + 1) [E] 𝑓(𝑦) = 𝑥² + 1

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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).

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