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Composition of functions worksheets Grade 10

Find f(g(x)) by putting all of g(x) in for x, working from the inside out.

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Free · Worked example · 18 problems · Answer key · US Letter

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How to do it

f(g(x)) means put all of g(x) in for x in f. Work from the inside out.

f(x)=−2x+1,g(x)=−x2−9;f(g(3))=37f(x) = -2x + 1,\quad g(x) = -x^{2} - 9;\quad f(g(3)) = 37
g(3)=−(3)2−9=−18g(3) = -(3)^{2} - 9 = -18inside first
f(−18)=−2(−18)+1=37f(-18) = -2(-18) + 1 = 37then the outside

Example problems

  1. f(x)=x2+2x+9,g(x)=−2x−7;f(g(−3))=f(x) = x^{2} + 2x + 9,\quad g(x) = -2x - 7;\quad f(g(-3)) =
  2. f(x)=−x,g(x)=3x+9;f(g(x))=f(x) = -x,\quad g(x) = 3x + 9;\quad f(g(x)) =
  3. f(x)=−2x2−2x−3,g(x)=x−4;f(g(x))=f(x) = -2x^{2} - 2x - 3,\quad g(x) = x - 4;\quad f(g(x)) =
  4. f(x)=−4x−8,g(x)=−2x2+4x−6;f(g(1))=f(x) = -4x - 8,\quad g(x) = -2x^{2} + 4x - 6;\quad f(g(1)) =

Functions

  1. Evaluating functions
  2. Finding the domain of a function
  3. Adding, subtracting and multiplying functions
  4. Composition of functions
  5. Inverse functions
  6. Transformations of functions
  7. Even and odd functions
  8. Average rate of change