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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
If f(x)=8x+110x-5 and g(x)=x-2, find (fg)(x), simplified, and state its domain.
  1. 8x-2+15(2x-1),  [2,)
  2. 8x-2+15(2x-1),  (-,12)(12,)
  3. 16x+10x-2-315(4x-9),  [2,94)(94,)
  4. 16x+10x-2-315(4x-9),  (-,94)(94,)
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Given (fg)(x)=1x24and g(x)=x2, find f(x).
  1. 1x4
  2. (1x2)4
  3. 1x24
  4. (1x)4
Grade 11 Functions and Relations CCSS: HSF-IF.A.2, HSF-BF.A.1, HSF-BF.A.1c
If f(x)=3x-4 and f(g(x))=x, then g(x) is
  1. 13x-4
  2. x+43
  3. 3-4x
  4. 4x-3
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Find (fg)(x) and state its domain, if f(x)=log(-x-5) and g(x)=x.
  1. log(-x-5),  x>0
  2. log(-x-5),  x<0
  3. log(-x-5),  x>25
  4. This composite function is not possible.
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If (f∘g)(x)=10x−2, which pair is valid?
  1. f(x)=2x−4,g(x)=5x+1
  2. f(x)=10x+10,g(x)=x−12
  3. Both A and B
  4. Neither A nor B
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Let f(x)=5x-2andg(x)=3x2+x. Find (gf)(x).
  1. 15xx+2-2
  2. 15x2+5x
  3. 3x(5x-2)x+2
  4. 15x-65x
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If (fg)(x)=x2+2x+4, which of the following could be the functions f(x) and g(x)? Choose all correct answers.
  1. f(x)=x2+3,  g(x)=x+1
  2. f(x)=x+2,  g(x)=x2+2x+2
  3. f(x)=x-5,  g(x)=x2+2x+9
  4. f(x)=x2+2,  g(x)=2x
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Let f(x)=3x2-5xandg(x)=x+2. Find (gf)(x).
  1. 3(x+2)-5x+2
  2. 3x2-5x+2
  3. -2x+6
  4. 3x-(5-1)x
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