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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
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
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
f(x)=x+43, g(x) = 3x − 4. Compute g(f(x)).
  1. x + 4
  2. x³
  3. x
  4. x3
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
The inverse of f(x) = 7 - x is f⁻¹(x) = 7 - x.
  1. True
  2. False
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
f(x)=x5+3, g(x) = 5x − 15. Compute g(f(x)).
  1. x5
  2. x + 3
  3. 5x
  4. 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
If f(x) = 2x, andg(x)=x2. Find f(g(x)).
Is g the inverse of f?
  1. Yes, f(g(x)) = x
  2. No, f(g(x)) = 4x²
  3. Yes, f(g(x)) = 2x
  4. No, f(g(x)) = x
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
f(x) = x² for x ≥ 0, g(x) = √x. What is f(g(x))?
  1. x
  2. |x|
  3. √x
  4. x²
Grade 11 Functions and Relations CCSS: HSF-BF.B.4b
Given f(x) = log(x²+1) and g(x) = √(10ˣ-1), is g = f⁻¹?
  1. True
  2. False
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