Define f : [0, 0) →R by f(x) = x. Find a function g: R → R such that gof is one-to-one, but g is not one-to-one.
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Please do part g. Please show step by step and explain
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- Prove that if f is a permutation on A, then (f1)1=f.For each of the following mappings f:ZZ, determine whether the mapping is onto and whether it is one-to-one. Justify all negative answers. a. f(x)=2x b. f(x)=3x c. f(x)=x+3 d. f(x)=x3 e. f(x)=|x| f. f(x)=x|x| g. f(x)={xifxiseven2x1ifxisodd h. f(x)={xifxisevenx1ifxisodd i. f(x)={xifxisevenx12ifxisodd j. f(x)={x1ifxiseven2xifxisoddGive an example of mappings and such that one of or is not onto but is onto.
- For each of the following pairs and decide whether is onto or one-to-one and justify all negative answers.Let f:AB and g:BA. Prove that f is one-to-one and onto if fg is one to-one and gf onto.Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove that f is one-to-one. Prove that f is onto if and only if a=1 or a=1.