CBSE Class 12-science - Composition of Functions Videos
Concepts related to composition of functions
Define composition of functions and establish the condition for a function to be invertible.
- 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) = ex. 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 = IR.
- 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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