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HSF.BF.B.4.b Tutor Intake — Verifying Inverses by Composition

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Grade 9·11 problems·~14 min·Common Core Math - HS Functions·standard·hsf-bf-b-4b

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Concepts

Consider $f(x) = x^2$ (with domain all real numbers) and $g(x) = \sqrt{x}$ .

Which statement best explains why $f$ and $g$ are NOT inverses over all real numbers?

$f(g(x)) \neq x$ for any value of $x$

$f(g(x)) = x$ for $x \geq 0$ , but $g(f(x)) = |x| \neq x$ for $x < 0$ , so one direction fails

Neither composition simplifies to $x$

$g(f(x)) = x$ for all real $x$ , but $f(g(x)) \neq x$