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Question Group Info

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Author: nsharp1
No. Questions: 4
Created: May 1, 2020
Last Modified: 5 years ago

Verifying Inverse Functions By Composition

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Let f(x)=x2 and g(x)=√x.
Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
A.
Find h(x)=f(g(x)) and state its domain.
  1. h(x)=x,  x≥0
  2. h(x)=|x|,  ℝ
  3. h(x)=x,  ℝ
  4. h(x)=|x|,  x≤0
Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
B.
Find h2(x)=g(f(x)) and state its domain.
  1. h2(x)=x,  x≥0
  2. h2(x)=|x|,  ℝ
  3. h2(x)=x,  ℝ
  4. h2(x)=|x|,  x≤0
Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
C.
Is g(x) the inverse of f(x)? Explain.
  1. Yes, since both h(x) and h2(x) are equal to x.
  2. No, because the domain of h(x) and h2(x) are different.
  3. No, because h(x)≠x.
  4. No, because h2(x)≠x.
Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b
D.
When finding h(x), what is the importance of the domain?
  1. It has no special importance.
  2. It shows that, even though h(x) and h2(x) seem to be the same function, they have different domains.
  3. It is necessary to see that the domain is all real numbers because the domain of inverse functions, when composed with the original function, needs to be all real numbers.
  4. It means that the absolute value sign can be dropped, since the domain is zero and positive numbers, so the function simply becomes x.