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Common Core Standard HSF-BF.B.4 Questions

Find inverse functions.

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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.4b

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Find [math]h_2(x) = g(f(x))[/math] and state its domain.
  1. [math]h_2(x) = x, \ \ x>=0[/math]
  2. [math]h_2(x) = |x|, \ \ RR[/math]
  3. [math]h_2(x) = x, \ \ RR[/math]
  4. [math]h_2(x) = |x|, \ \ x<=0[/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.4b

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Is [math]g(x)[/math] the inverse of [math]f(x)?[/math] Explain.
  1. Yes, since both [math]h(x)[/math] and [math]h_2(x)[/math] are equal to [math]x[/math].
  2. No, because the domain of [math]h(x)[/math] and [math]h_2(x)[/math] are different.
  3. No, because [math]h(x) != x[/math].
  4. No, because [math]h_2(x) != x[/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 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b

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When finding [math]h(x)[/math], what is the importance of the domain?
  1. It has no special importance.
  2. It shows that, even though [math]h(x)[/math] and [math]h_2(x)[/math] 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 [math]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]
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