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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
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.4, HSF-BF.B.4c
What is f⁻¹(0.5) 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.4d
Given f(x) = |x + 2| Which domain makes f(x) invertible?
  1. x ≥ −2
  2. x ≤ 0
  3. x > −2
  4. x ≤ −2
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
The graph is plotted for y = cos(x) with domain 0 ≤ x ≤ π.
Why is this standard restriction used for cos⁻¹(x)?
  1. It captures all output values
  2. It makes the function one-to-one
  3. It's continuous
  4. All of the above
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
Is f(x)=2x one-to-one?
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
Is the combined function invertible?
  1. Yes
  2. No
  3. Only if restricted further
  4. Only for x > 1
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
Is f(x) = |x| invertible?
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4c
What is f-1(7)?
  1. 1
  2. 2
  3. 3
  4. 4
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4c
If f contains these points, what is f-1(5)?
  1. 1
  2. 2
  3. 3
  4. 5
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4c
What is f⁻¹(16)?
  1. 5
  2. 7
  3. 9
  4. 11
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse. f(x)=x-8x+1
  1. f-1(x)=x-1x+8
  2. f-1(x)=-9x+1
  3. f-1(x)=-x-8x-1
  4. f-1(x)=x-8x
Grade 11 Functions and Relations CCSS: HSF-BF.B.4
Find the inverse of f(x)=x-24.
  1. f⁻¹(x) = 4x + 2
  2. f⁻¹(x) = 4x - 2
  3. f⁻¹(x)=x+24
  4. f⁻¹(x)=x-24
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of f(x) = 5eˣ
  1. f⁻¹(x)=ln(x5)
  2. f⁻¹(x)=ln(5x)
  3. f⁻¹(x)=eˣ5
  4. f⁻¹(x)=ln(x)-5
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of f(x) = 6 − 2x
  1. f⁻¹(x)=x−62
  2. f⁻¹(x)=6−x2
  3. f⁻¹(x) = 6 + 2x
  4. f⁻¹(x)=3−x2
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