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Asked by Yashraj Last Modified
Answer To prove that the function f:R→Rf:R→R given by f(x)=2xf(x)=2x is one-to-one (injective), we need to show that if f(x1)=f(x2)f(x1)=f(x2), then x1=x2x1=x2 for all x1,x2x1,x2 in the domain.
Let's assume f(x1)=f(x2)f(x1)=f(x2): 2x1=2x22x1=2x2
Now, we'll solve for x1x1 and x2x2: x1=x2x1=x2
Since x1=x2x1=x2, it means that for any two inputs x1x1 and x2x2 that produce the same output under the function f(x)=2xf(x)=2x, those inputs must be the same. This proves that the function f(x)=2xf(x)=2x is one-to-one.
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