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Class 12

Composition, Inverses and Mixed Practice — Quiz

Five questions on composite and inverse functions. Pick one answer for each.

5 questions, one mark each. 3 to pass. Suggested time: 10 minutes. Your answers are not recorded.

  1. If f(x)=3x−2f(x) = 3x - 2 and g(x)=x2g(x) = x^2, then (g∘f)(x)(g \circ f)(x) equals
  2. Find f−1f^{-1} for f:R→Rf : \mathbf{R} \to \mathbf{R}, f(x)=5x+3f(x) = 5x + 3.
  3. f={(1,4),(2,6),(3,5)}f = \{(1, 4), (2, 6), (3, 5)\} and g={(4,2),(5,1),(6,3)}g = \{(4, 2), (5, 1), (6, 3)\}. Find g∘fg \circ f.
  4. If f(x)=x+4f(x) = x + 4 and g(x)=x2−1g(x) = x^2 - 1, find (f∘g)(2)(f \circ g)(2).
  5. Which function f:{1,2,3}→{a,b,c}f : \{1, 2, 3\} \to \{a, b, c\} is invertible?
Unanswered questions are marked wrong.