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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
f(x) = sin(x), g(x) = arcsin(x), where −π/2 ≤ x ≤ π/2. Find f(g(x)).
  1. sin(x)
  2. x
  3. arcsin(x)
  4. π/2
Grade 11 Functions and Relations CCSS: HSF-BF.B.4b
Find the inverse of g(x) = √(x - 3).
  1. g⁻¹(x) = (x²) + 3
  2. g⁻¹(x) = (x²) - 3
  3. g⁻¹(x) = √(x + 3)
  4. g⁻¹(x) = (x²)/3
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
f(x) = x³ + 1, g(x)=3√x−1. Compute f(g(x)).
  1. x
  2. x³
  3. 3√x
  4. x - 1
Grade 11 Functions and Relations CCSS: 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 h(x) = f(g(x)) and state its domain.
Let f(x) = x³ and g(x) = ∛x.
  1. h(x) = x, x ≥ 0
  2. h(x) = x, ℝ
  3. h(x) = |x|, ℝ
  4. h(x) = x³, ℝ
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
Find h(x) = f(g(x)) and its domain.
  1. h(x) = x, x ≠ 0
  2. h(x) = 1/x², x ≠ 0
  3. h(x) = x, ℝ
  4. h(x) = 1/x, x ≠ 0
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
f(x) = 7x − 2, g(x)=x+27. Compute f(g(x)).
Is g the inverse of f?
  1. No, f(g(x)) = x − 2
  2. No, f(g(x)) = x + 2
  3. Yes, f(g(x)) = 7x
  4. Yes, f(g(x)) = x
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
f(x) = tan(x), g(x) = arctan(x), for −π/2 < x < π/2. Find f(g(x)).
  1. x
  2. tan(x)
  3. arctan(x)
  4. π/2
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 g(x)=1xthe inverse of f(x)=1x?
  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
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