CBSE Class 12 science: Composition of Functions Videos | Concepts related to composition of functions

• Show that f:A-B and g:B-C are onto function then g°f:A-C is onto function?
• Define invertible function.
• Let   be the functions defined as f(1) = 3, f(3) = 4, f(5) = f(7) = 8 and g(3) = g(4) = 7 and g(6) = g(8) = 10. Find gof.
• If  are defined as f(x) = cos x and g(x) = x². Show that .
• If  and  are one-one functions, then show that  is also one-one.
• If are defined as f(x) = log (1 + x) and g(x) = e^x. Find fog(x) and gof(x).
• If  is defined as f(x) = x³ – 2. Find f^–1(62).
• Let be defined by f(x) = 3x – 2 and be defined by Show that fog = I_R.
• Let given by . Show that f is invertible with
• If show that fof(x) = x for all . Also find the inverse of f.

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