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Common Core Standard HSF-BF.B.4a Questions

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠ 1.

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Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of the following function. [math]f(x) = 4x^3 + 2[/math]
  1. [math]f^{-1}(x) = (x^3-2)/4[/math]
  2. [math]f^{-1}(x) = (root[3](x) - 2)/4[/math]
  3. [math]f^{-1}(x) = root[3]((x-2)/4) [/math]
  4. [math]f^{-1}(x) = root[3](x-2)/4[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
What is the inverse of [math]f(x) = (5x - 1) / 2[/math]?
  1. [math]f⁻¹(x) = (2x - 1) / 5 [/math]
  2. [math]f⁻¹(x) = (5x + 1) / 2 [/math]
  3. [math]f⁻¹(x) = (2x + 1) / 5 [/math]
  4. [math]f⁻¹(x) = (5x - 1) / 2 [/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of [math]f(x) = (x + 3)/4[/math].
  1. [math](x - 3)/4[/math]
  2. 4x + 3
  3. 4x - 3
  4. [math](x + 3)/4[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of:[math] g(x) = 1/2ln(2x) - 3[/math].
  1. [math]g⁻¹(x) = (e^(2(x + 3)))/2[/math]
  2. [math] g⁻¹(x) = e^(1/2x + 3)/2[/math]
  3. [math] g⁻¹(x) = 2e^(2x) + 3[/math]
  4. [math]g⁻¹(x) = (e^(x + 3))/4[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of: h(x) = (x + 1)/(x - 1), x ≠ 1
  1. h⁻¹(x) = (x - 1)/(x + 1)
  2. h⁻¹(x) = (x + 1)/(x - 1)
  3. h⁻¹(x) = (1 + x)/(1 - x)
  4. h⁻¹(x) = (1 - x)/(1 + x)
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of f(x) = (x + 3)/(2x − 1).
  1. [math]f⁻¹(x) = (x + 1)/(2x − 3)[/math]
  2. [math]f⁻¹(x) = (x + 1)/(3− 2x)[/math]
  3. [math]f⁻¹(x) = (x + 1)/(2x +3)[/math]
  4. [math]f⁻¹(x) = (x -1)/(2x − 3)[/math]
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]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of [math]f(x) = (2x + 1) / 5[/math]
  1. [math]f⁻¹(x) = (5x − 1) / 2[/math]
  2. [math]f⁻¹(x) = (5x + 1) / 2[/math]
  3. [math]f⁻¹(x) = (2x − 1) / 5[/math]
  4. [math]f⁻¹(x) = (5x − 2) / 3[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of [math]f(x) = 2e^x- 3[/math].
  1. [math]f⁻¹(x) = ln((x + 3)/2)[/math]
  2. [math]f⁻¹(x) = ln(x/2) + 3[/math]
  3. [math]f⁻¹(x) = e^(x/2) + 3[/math]
  4. f⁻¹(x) = ln(x + 3) - 2
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of: g(x) = -3x + 6.
  1. [math]g⁻¹(x) = (6 - x)/3[/math]
  2. [math]g⁻¹(x) = (x - 6)/3[/math]
  3. g⁻¹(x) = -3x + 6
  4. [math]g⁻¹(x) = (x + 6)/3[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of: [math]p(x) = 10^(x + 2) - 5[/math].
  1. [math]p⁻¹(x) = log_10(x + 5) - 2[/math]
  2. [math]p⁻¹(x) = log_10x + 5 - 2[/math]
  3. [math]p⁻¹(x) = (x + 5)/10 - 2[/math]
  4. [math]p⁻¹(x) = log_10(x - 5) - 2[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
What is the inverse of [math]f(x) = 2^x + 4[/math]?
  1. [math]f⁻¹(x) = log_2(x − 4)[/math]
  2. [math]f⁻¹(x) = log_2(x + 4)[/math]
  3. [math]f⁻¹(x) = 2^(x − 4)[/math]
  4. [math]f⁻¹(x) = 2^(x + 4)[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of the following function. [math]f(x) = 3^{9x-5}[/math]
  1. [math]f^{-1}(x) = log_3(1/9 x + 5)[/math]
  2. [math]f^{-1}(x) = log_3(x/9) + 5[/math]
  3. [math]f^{-1}(x) = log_3(x+5)/9[/math]
  4. [math]f^{-1}(x) = (log_3(x) + 5)/9[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of f(x) = ln(3x - 1)
  1. [math]f⁻¹(x) = (eˣ + 1) / 3[/math]
  2. [math]f⁻¹(x) = e^x/ 3 + 1[/math]
  3. f⁻¹(x) = ln(3x) + 1
  4. [math] f⁻¹(x) = 3e^x - 1[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of h(x) = { 2x if x ≥ 0; -x if x < 0 }.
  1. { [math] 1/2[/math] x if x > 0; -x if x ≤ 0 }
  2. { [math] x/2[/math] if x > 0; x if x ≤ 0 }
  3. { [math] 1/2[/math] x if x ≥ 0; x if x < 0 }
  4. { [math] x/2[/math] if x ≥ 0; -x if x < 0 }
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of: [math]h(x) = 1/2x - 4[/math].
  1. h⁻¹(x) = 2x + 4
  2. [math]h⁻¹(x) = 1/2(x + 4)[/math]
  3. h⁻¹(x) = 2(x + 4)
  4. [math]h⁻¹(x) = 1/2x + 4[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of: h(x) = { 3x if x ≥ 0; -2x if x < 0 }
  1. h⁻¹(x) = {[math] 1/3 [/math] x if x > 0; ½x if x ≤ 0 }
  2. h⁻¹(x) = { [math] x/3 [/math] if x > 0; x/2 if x ≤ 0 }
  3. h⁻¹(x) = { [math] 1/3 [/math] x if x ≥ 0; -1/2x if x < 0 }
  4. h⁻¹(x) = {[math] x/3 [/math] if x ≥ 0; -x/2 if x < 0 }
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of [math]f(x) = (3x − 2)/5[/math].
  1. [math]f⁻¹(x) = (3x + 2)/5[/math]
  2. [math]f⁻¹(x) = (3x - 2)/5[/math]
  3. [math]f⁻¹(x) = (5x - 2)/3[/math]
  4. [math]f⁻¹(x) = (5x + 2)/3[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
If [math]f(x) = log_4(3x-1) + 10[/math], what is the inverse of this function?
  1. [math]f^{-1}(x) = (4^(x-10)+1)/3[/math]
  2. [math]f^{-1}(x) = 4(x/3 + 1) - 10[/math]
  3. [math]f^{-1}(x) = 1/3 (4^x -9)[/math]
  4. [math]f^{-1}(x) = 4^((x-10)/3 + 1)[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
What is the inverse of [math]f(x) = √(x - 3)[/math], x ≥ 3?
  1. [math]f⁻¹(x) = x^2 - 3 [/math]
  2. [math]f⁻¹(x) = x^2 + 3 [/math]
  3. f⁻¹(x) = x + 3
  4. [math]f⁻¹(x) = (x + 3)^2 [/math]
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