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Common Core Standard HSF-BF.B.4 Questions

Find inverse functions.

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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) = |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.4a
Find the inverse off(x)=10x-2
  1. f⁻¹(x)=10x+2
  2. f⁻¹(x)=log10(x-2)
  3. f⁻¹(x)=log10(x)+2
  4. f⁻¹(x)=log10(2x)
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of h(x)=12x+6.
  1. 2(x - 6)
  2. 12(x-6)
  3. 2x - 6
  4. (12x)-6
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of: f(x) = |x + 3|, x ≥ -3
  1. f⁻¹(x) = |x| - 3
  2. f⁻¹(x) = -x - 3
  3. f⁻¹(x) = x - 3
  4. f⁻¹(x) = x + 3
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
If h(x) = √(x − 3), what is h⁻¹(x)?
  1. h⁻¹(x) = x² + 3
  2. h⁻¹(x) = x + 3
  3. h⁻¹(x) = x² − 3
  4. h⁻¹(x) = (x + 3)²
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
If h(x)=(x+2)2, x ≥ −2, find h⁻¹(x):
  1. h⁻¹(x)=√x+2
  2. h⁻¹(x)=-√x−2
  3. h⁻¹(x)=√x−2
  4. h⁻¹(x)=√x−2
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
f(x)=log2(x), g(x) = 2ˣ. Compute f(g(x)).
  1. x²
  2. log2(x)
  3. 2ˣ
  4. x
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4c
What is f⁻¹(4.1) from the table below?
  1. 1
  2. 2
  3. 3
  4. 4
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
If f(x)=log4(3x-1)+10, what is the inverse of this function?
  1. f-1(x)=4x-10+13
  2. f-1(x)=4(x3+1)-10
  3. f-1(x)=13(4x-9)
  4. f-1(x)=4x-103+1
Grade 11 Functions and Relations CCSS: HSF-BF.B.4
The following table shows values for k(x):
Find k⁻¹(2).
  1. -1
  2. 0
  3. 2
  4. 1
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.4a
Find the inverse of f(x)=1x−2, x ≠ 2.
  1. f⁻¹(x)=(1x)+2
  2. f(x)=1x+2
  3. f(x)=1x−2
  4. f⁻¹(x) = x + 2
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of g(x)=2x-15.
  1. 5x-12
  2. 5x+12
  3. 2x+15
  4. 5x+12
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of: f(x) = 5x + 2.
  1. f⁻¹(x)=x+25
  2. f⁻¹(x)=x-25
  3. f⁻¹(x) = 5x - 2
  4. f⁻¹(x)=x5-2
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