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Common Core Standard HSF-BF.A.1c Questions

(+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.

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Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
[math]f(x) = sqrt(x+3)[/math] and [math]g(x)=2x[/math]. Find [math](f @ g)(4)[/math].
  1. [math]2sqrt14[/math]
  2. [math]sqrt11[/math]
  3. [math]sqrt14[/math]
  4. [math]2sqrt7[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If [math] g(x) = 4/(2-x) and (g@f)(x) = -2/x^2[/math], find [math]f(x)[/math].
  1. [math](2x^2)/(x^2+1)[/math]
  2. [math](x-2)/x^2[/math]
  3. [math]2x^2 + 2[/math]
  4. [math]-1/(2(x^2 - 2))[/math]
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
What are possible function rules for [math]f(x)[/math] and [math]g(x)[/math], if [math](g@f)(x) = 9x^2 - 15x -13 ?[/math] There may be more than one correct answer.
  1. [math]f(x) = x-2, \ \ g(x) = 9x^2+21x-7[/math]
  2. [math]f(x) = 3x+2, \ \ g(x) = x^2 - 9x + 1[/math]
  3. [math]f(x) = 3x^2 -5x - 5, \ \ g(x) = 3x-2[/math]
  4. [math]f(x) = 3x^2 - 5x - 13, \ \ g(x) = 3x[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
[math]f(x) =7x+9 and g(x) = 4x-1[/math]. Find [math](f @ g)(x)[/math].
  1. [math]28x+8[/math]
  2. [math]28x+16[/math]
  3. [math]28x+2[/math]
  4. [math]28x+35[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Find the domain of the composite function [math](f@g)(x) if f(x)=x^2 and g(x)=sqrt(x+2)[/math].
  1. [math](-oo,oo)[/math]
  2. [math](-2,oo)[/math]
  3. [math][-2,oo)[/math]
  4. [math](-oo,-2)[/math]
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If [math](f@g)(x) = 10x - 2[/math], which of the following are possible function rules for [math]f(x)[/math] and [math]g(x) ?[/math] Choose all correct answers.
  1. [math]f(x) = 10x + 10, \ \ g(x) = x - 12[/math]
  2. [math]f(x) = 2x-4, \ \ g(x) = 5x+1[/math]
  3. [math]f(x) = 8x-9, \ \ g(x) = 5/4 x - 11/4[/math]
  4. [math]f(x) = 1/2x - 3 \ \ g(x) = 20x + 2[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
[math]f(x)=6/(x-4) and g(x)= 5/(4x)[/math]. Find [math](f @ g)(x)[/math].
  1. [math](24x)/(5-16x)[/math]
  2. [math](24x)/(5+16x)[/math]
  3. [math](6x)/(5-16x)[/math]
  4. [math](5x-20)/(24x)[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Let [math]f(x) = 5x-1 and g(x) = 3x^2 + 2x - 1[/math]. Find [math](g@f)(x)[/math].
  1. [math]75x^2 - 20x[/math]
  2. [math]15x^2+10x-6[/math]
  3. [math]75x^2-28x+2[/math]
  4. [math]25x-3[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
For [math](f@g)(x) = e^(-x^2 + 6)[/math], which of the following are possible function rules of [math]f(x)[/math] and [math]g(x) ?[/math] There may be more than one correct answer.
  1. [math]f(x) = e^x, \ \ g(x) = -x^2 + 6[/math]
  2. [math]f(x) = e^(-x+6), \ \ g(x) = x^2[/math]
  3. [math]f(x) = e^(-x^2 - 4x + 2), \ \ g(x) = x-2[/math]
  4. [math]f(x) = x^2, \ \ g(x) = e^(-1/2x^2 + 3)[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
[math]f(x) = sqrt(x+8) and g(x)= 8x-12[/math]. Find [math](f @ g)(x)[/math].
  1. [math]2sqrt(2x-1)[/math]
  2. [math]8sqrt(x+8)-12[/math]
  3. [math]8sqrt(x-4)[/math]
  4. [math]2sqrt(2x+1)[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Which of the following could be the function rules for [math]f(x)[/math] and [math]g(x)[/math] if [math](f@g)(x) = sqrt(x^3-8) ?[/math] There may be more than one correct answer.
  1. [math]f(x) = sqrt(x), \ \ g(x) = x^2 - 8[/math]
  2. [math]f(x) = sqrt(x^2-8), \ \ g(x) = x[/math]
  3. [math]f(x) = sqrt(x-8), \ \ g(x) = x^3[/math]
  4. [math]f(x) = sqrt(x^3), \ \ g(x) = x-2[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
[math]f(x) = 3x-12 and g(x) = 4x[/math]. Find [math](f @ g)(x)[/math].
  1. [math]12x^2+48x[/math]
  2. [math]12x-48[/math]
  3. [math]12x-12[/math]
  4. [math]7x-12[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Find [math](f@g)(x)[/math] and state its domain if [math]f(x) = 3x^2 + 5x - 3[/math] and [math]g(x) = 4x-1[/math].
  1. [math]48x^2 - 4x - 5, \ \ RR[/math]
  2. [math]48x^2 - 19x, \ \ RR[/math]
  3. [math]3x^2 + 20x-8, \ \ x!=1/4[/math]
  4. [math]48x^2 - 4x - 5, \ \ x!= 1/4[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If [math](f@g)(x) = x^4 - 6x^2 + 7x + 9[/math], which of the following are possible functions rules for [math]f(x)[/math] and [math]g(x) ?[/math] There may be more than one correct answer.
  1. [math]f(x) = x^2 + 7x, \ \ g(x) = x^2 - 3[/math]
  2. [math]f(x) = x^2, \ \ g(x) = x^2 +7/3 x + 3[/math]
  3. [math]f(x) = x+3, \ \ g(x) = x^4 - 6x^2 + 7x + 6[/math]
  4. [math]f(x) = x^4 + x^3 - 17/4, \ \ g(x) = x - 1/4[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
[math]f(x)= 2x+6 and g(x) = 4x+2[/math]. Find [math](g @ f)(x)[/math].
  1. [math]8x+26[/math]
  2. [math]8x+10[/math]
  3. [math]6x+8[/math]
  4. [math]6x+12[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Find [math](g@f)(x)[/math] and state its domain if [math]f(x) = (3x-5)/(9x-1)[/math] and [math]g(x) = 3x + 4[/math].
  1. [math](9x+7) / (27x + 35), \ \ x!= -27/35[/math]
  2. [math](9x+7) / (9x - 1), \ \ x!= 1/9[/math]
  3. [math](9x+7) / (27x+35), \ \ x!= -35/27[/math]
  4. [math](45x-19) / (9x-1), \ \ x!=1/9[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Select the possible function rules of [math]f(x)[/math] and [math]g(x)[/math] if [math](f@g)(x) = x^2 - 4[/math]. Choose all correct answers.
  1. [math]f(x) = ln(x), \ \ g(x) = e^(x^2-4)[/math]
  2. [math]f(x) = ln(x^2), \ \ g(x) = e^(1/2 x^2 -2)[/math]
  3. [math]f(x) = ln(x^2 - 8), \ \ g(x) = e^(1/2 x^2 + 2)[/math]
  4. [math]f(x) = e^x - 8, \ \ g(x) = ln(x^2+4)[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If [math]f(x) = x^2 + 3[/math] and [math]g(x) = sqrt(x-4)[/math] find [math](f@g)(x)[/math] and state its domain.
  1. [math]x-1, \ \ x >= 4[/math]
  2. [math]sqrt(x^2 - 1), \ \ x < -1 or x > 1[/math]
  3. [math]x+1, \ \ x >= 4[/math]
  4. [math]x+1, \ \RR[/math]
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