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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) = 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
For [math]f(x) = 1/x[/math] and g(x) = x − 1, the domain of (g∘f)(x) is__.
  1. x ≠ 0
  2. x ≠ 1
  3. All real numbers
  4. x > 0
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
For f(x) = √(x+1) and g(x) = x² - 1, find (f∘g)(2).
  1. √3
  2. 2
  3. 3
  4. 1
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
For [math]f(x)=sqrt x[/math] and [math]g(x)=x^2+8[/math], the domain of (f∘g)(x)is:
  1. x≥0
  2. All real numbers
  3. x≤−22
  4. x≥2.828
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Given [math]f(x) = e^x[/math] and g(x) = ln x, what is (f∘g)(e²)?
  1. [math]e^2[/math]
  2. 2
  3. [math]e^(e^2) [/math]
  4. ln 2
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
For [math]f(x) = 1/(x-2)[/math] and g(x) = x + 3, the domain of (f∘g)(x) is:
  1. x ≠ -1
  2. x ≠ 2
  3. x ≠ 5
  4. All real numbers
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Given [math]f(x) = 1/(x+2)[/math] and g(x) = x - 3, the domain of (f∘g)(x) is:
  1. x ≠ 1
  2. x ≠ -2
  3. x ≠ 3
  4. All real numbers
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]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If [math](f@g)(x) = 2|x+6|[/math], what are possible function rules for [math]f(x)[/math] and [math]g(x) ?[/math] There may be more than one correct answer.
  1. [math]f(x) = sqrt(x), \ \ g(x) = 4x^2 + 48x + 144[/math]
  2. [math]f(x) = sqrt(x^2 + 6), \ \ g(x) = 2x[/math]
  3. [math]f(x) = 4x^2 + 6, \ \ g(x) = 1/2sqrt(x)[/math]
  4. [math]f(x) = x^2 + 6, \ \ g(x) = 2sqrt(x)[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Given [math](f∘g)(x)=4x^2−12x+9[/math], which pair could be f and g?
  1. [math] f(x)=2x−3 , g(x)=x^2[/math]
  2. [math] f(x)=x^2 , g(x)=2x-3[/math]
  3. [math] f(x)=4x+9 , g(x)=2x^2-3x[/math]
  4. [math] f(x)=2x−3 , g(x)=4x^2-12x+9[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If f(x) = sin x and [math]g(x) = π/2 − x[/math], what is (f∘g)(0)?
  1. 0
  2. 1
  3. -1
  4. [math]π/2[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Given [math]f(x) = e^x [/math] and g(x) = ln(x), find (f∘g)([math]e^5[/math]).
  1. [math]e^5[/math]
  2. 5
  3. [math]e^(e^5) [/math]
  4. 1
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