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Common Core Standard HSF-BF.B.4b Questions

(+) Verify by composition that one function is the inverse of another.

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Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
Find h₂(x) = g(f(x)) for f(x) = x³ and g(x) = ∛x.
  1. h₂(x) = x, x ≥ 0
  2. h₂(x) = x, ℝ
  3. h₂(x) = |x|, ℝ
  4. h₂(x) = x³, ℝ
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
Is [math]g(x) = 1/x [/math]the inverse of [math]f(x) = 1/x[/math]?
  1. Yes, because h(x) = h₂(x) = x
  2. No, because f(g(0)) is undefined
  3. Only for x > 0
  4. No, because their ranges differ
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
Is g(x) = ∛x the inverse of f(x) = x³?
  1. Yes, because h(x) = h₂(x) = x for all real numbers
  2. No, because their domains differ
  3. Only for x ≥ 0
  4. No, because h₂(x) ≠ x
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
Find h(x) = f(g(x)).
  1. h(x) = x², ℝ
  2. h(x) = |x|, ℝ
  3. h(x) = x⁴, ℝ
  4. h(x) = x², x ≥ 0
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
Find h₂(x) = g(f(x)) for f(x) = |x| and g(x) = x².
  1. h₂(x) = x², ℝ
  2. h₂(x) = |x|, ℝ
  3. h₂(x) = x⁴, ℝ
  4. h₂(x) = x², x ≥ 0
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
Why isn't g(x) = x² the inverse of f(x) = |x|?
  1. Because h(x) ≠ h₂(x)
  2. Because f(g(-1)) = 1 ≠ -1
  3. Because their domains differ
  4. Both a and b
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