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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
Find the inverse of g(x) = -2x + 5.
  1. [math]g⁻¹(x) = (x - 5)/2[/math]
  2. [math]g⁻¹(x) = (x - 5)/-2[/math]
  3. [math]g⁻¹(x) = (5 - x)/2[/math]
  4. [math]g⁻¹(x) = (5 + x)/-2[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
Let f(x) = |x| and g(x) = x².
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.4a
What is the inverse of [math]f(x) = 1 / (x + 2)[/math], x ≠ -2?
  1. [math]f⁻¹(x) = (1 / x) - 2[/math]
  2. [math]f⁻¹(x) = (1 / x) + 2[/math]
  3. [math]f⁻¹(x) = 1 / (x + 2)[/math]
  4. f⁻¹(x) = x + 2
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of [math]p(x) = 5(10^(x^+3)[/math].
  1. [math]p⁻¹(x) = log_10(x - 5) + 3[/math]
  2. [math]p⁻¹(x) = log_10(x) - 5 - 3[/math]
  3. [math]p⁻¹(x) = (log_10x)/5 - 3[/math]
  4. [math]p⁻¹(x) = log_10(x/5) - 3[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of: [math]g(x) = (4x - 1)/7[/math].
  1. [math]g⁻¹(x) = 7x + 1/4[/math]
  2. [math] g⁻¹(x) = (4x + 1)/7[/math]
  3. [math] g⁻¹(x) = (7x - 1)/4[/math]
  4. [math] g⁻¹(x) = (7x + 1)/4[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of g(x) = (x − 2)/(x + 1), x ≠ −1
  1. g⁻¹(x) = (2 − x)/(x − 1)
  2. g⁻¹(x) = (x + 2)/(1 − x)
  3. g⁻¹(x) = (2 + x)/(x − 1)
  4. g⁻¹(x) = (x − 2)/(x + 1)
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of [math]f(x) = (x − 5)^3[/math].
  1. [math]f⁻¹(x) = 3sqrt x + 5[/math]
  2. [math]f⁻¹(x) = 3sqrt (x + 5)[/math]
  3. [math]f⁻¹(x) = (x + 5)^3[/math]
  4. [math]f⁻¹(x) = (x - 5)^3[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
f(x) = cos(x), g(x) = arccos(x), where 0 ≤ x ≤ π. Find f(g(x)).
  1. cos(x)
  2. x
  3. arccos(x)
  4. π
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
f(x) = 5 − 3x, [math]g(x) = (5 − x)/3[/math]. Find f(g(x)).
  1. x
  2. 5 − x
  3. x - 3
  4. -3x
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4c
What is f⁻¹(4)?
  1. 1
  2. 2
  3. -2
  4. 16
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
What is the equation of the inverse function after restriction?
  1. y = √x
  2. y = -√x
  3. y = x²
  4. y = ±√x
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
Given [math]f(x) = 1 / x^2[/math] Which domain makes f(x) invertible?
  1. x > 0
  2. x < 0
  3. Both A and B
  4. x ≠ 0
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
What is the inverse of [math]f(x) = 3/(x-1) ?[/math]
  1. [math]f^{-1}(x) = (x+1)/3[/math]
  2. [math]f^{-1}(x) = (x+3)/x[/math]
  3. [math]f^{-1}(x) = 3/(x+1)[/math]
  4. [math]f^{-1}(x) = 4/x[/math]
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