Maths · One-one, into and onto functions
is defined by =\mathbf{1 5} \boldsymbol{x}+\mathbf{7} \) is
\( \boldsymbol{f}: \boldsymbol{Q} \rightarrow \boldsymbol{Q} \) is defined by \( \boldsymbol{f}(\boldsymbol{x})=\mathbf{1 5} \boldsymbol{x}+\mathbf{7} \) is
- A. injective only
- B. surjective only
- C. bijective
- D. neither injective nor surjective
Step-by-step solution
The function f(x)=15x+7 from Q to Q is injective because if 15a+7=15b+7 then a=b. It is surjective because for any y in Q, x=(y-7)/15 is in Q. Hence it is bijective.
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