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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. [math]f(x) = 1/5 x^3[/math]
  1. [math]f^{-1}(x) = 5root[3](x)[/math]
  2. [math]f^{-1}(x) = root[3](5x)[/math]
  3. [math]f^{-1}(x) = root[3](1/5 x)[/math]
  4. [math]f^{-1}(x) = 1/5root[3](x)[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse. [math]f(x) = (x-8)/(x+1)[/math]
  1. [math]f^{-1}(x) = (x-1)/(x+8)[/math]
  2. [math]f^{-1}(x) = -9/(x+1)[/math]
  3. [math]f^{-1}(x) = (-x-8)/(x-1)[/math]
  4. [math]f^{-1}(x) = (x-8)/x[/math]
Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of [math]f(x) = 1/2 x + 4/5[/math].
  1. [math]f^{-1}(x) = 2x - 8/5[/math]
  2. [math]f^{-1}(x) = 2x - 4/5[/math]
  3. [math]f^{-1}(x) = -1/2 x - 4/5[/math]
  4. [math]f^{-1}(x) = -2x - 5/4[/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) = e^(x^3)[/math]
  1. This function has no inverse.
  2. [math]f^{-1}(x) = ln(x^3)[/math]
  3. [math]f^{-1}(x) = ln(root[3](x))[/math]
  4. [math]f^{-1}(x) = root[3](ln(x))[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of [math]g(x)=-3x[/math].
  1. [math]g ^(-1) (x)=x+1[/math]
  2. [math]g ^-1 (x)=-3x-3[/math]
  3. [math]g ^-1 (x)=x-1[/math]
  4. [math]g ^-1(x)= -1/3 x[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of the function [math]g(x) = -4x + 1[/math].
  1. [math]g^(-1)(x) = 1 /(x+3) [/math]
  2. [math]g^(-1)(x) = 3 /(x+2) [/math]
  3. [math]g^(-1)(x) = 1 /(x+2) [/math]
  4. [math]g^(-1)(x) = (-x+1) /4 [/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Which is the inverse of [math]f(x)=2x-7[/math]?
  1. [math]f^-1(x)=2/7(x+1)[/math]
  2. [math]f^-1(x)=2/7x+7[/math]
  3. [math]f^-1(x)=(x+7)/2[/math]
  4. [math]f^-1(x)=x/2+7[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse for the function.
[math]f(x)=-3/4x+5[/math]
  1. [math]f^-1(x)=(3x-5)/4[/math]
  2. [math]f^-1(x)=3/4(x-5)[/math]
  3. [math]f^-1(x)=(-4x-5)/3[/math]
  4. [math]f^-1(x)=(-4x+20)/3[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Match each function with its inverse.
__ [math]f(x) = 3 ln(x+2) [/math] A. [math]f^{-1} (x) = e^(x//3) -2 [/math]
__ [math]f(x) = e^(5x+2) [/math] B. [math]f^{-1} (x) = (ln(x)-2)/5 [/math]
__ [math]f(x) = log(3x)/2 [/math] C. [math]f^{-1} (x) = log(x-5) + 2[/math]
__ [math]f(x) = 10^{x-2} + 5[/math] D. [math]f^{-1} (x) = 10^{2x}/3 [/math]
Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of the function [math]f(x) = 3x-2[/math].
  1. [math]f^{-1}(x) = 1/3 x + 2[/math]
  2. [math]f^{-1}(x) = x +2 [/math]
  3. [math]f^{-1}(x) = x + 2/3[/math]
  4. [math]f^{-1}(x) = 1/3 x + 2/3[/math]
Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of [math]f(x) = x[/math].
  1. [math]f^{-1}(x) = x[/math]
  2. [math]f^{-1}(x) = y[/math]
  3. [math]f^{-1}(x) = 1[/math]
  4. [math]f^{-1}(x) = 1/x[/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) = 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) = 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 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
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
Which of the following functions is the inverse of [math]y=3x+5[/math]?
  1. [math]-y=-3x-5[/math]
  2. [math]y=(x-5)/3[/math]
  3. [math]x=3y+5[/math]
  4. [math]y=1/3x-5[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Which of the following is the inverse of [math]y=(5x^2+4)/3, x>=0[/math]?
  1. [math]-y=+-sqrt(5x^2)+3/4[/math]
  2. [math]-y=(-5x^2-4)/-3[/math]
  3. [math] x=(5y^2+4)/3[/math]
  4. [math]y=sqrt((3x-4)/5)[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Which of the following is the inverse of [math]y=x^2+4, x<=0[/math] ?
  1. [math]-y=sqrt(x-4)[/math]
  2. [math]y=+-sqrt(x)-2[/math]
  3. [math]x=+-sqrt(y^2+4)[/math]
  4. [math]y=sqrt(x)-4[/math]

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