Back to Restrict domain for invertibility — Problem 1 · Task Set 45

HSF.BF.B.4.d Tutor Intake — Domain Restriction and Invertible Functions

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Grade 9·10 problems·~14 min·Common Core Math - HS Functions·standard·hsf-bf-b-4d

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Concepts

The function $f(x) = x^2$ does NOT have an inverse on its full domain.
Which statement BEST explains why?

The graph does not pass the vertical line test

Two different inputs produce the same output — for example,
$f(3) = 9$ and $f(-3) = 9$ — so the inverse cannot assign a unique
input to the output $9$

The function is not continuous

The inverse of $x^2$ does not have an equation