Question

Which of the following functions are bijections?

• A. f: R→ R ; f(x) = Sin(x)
• B. g : R → R ; g(x) = x
• C. h: R →R ; h(x) = a^x where a >1
• D. k: R→[-1,1] ; k(x) = Cos(x)

Answer 1

The correct option is B

g : R → R ; g(x) = x

We’ll answer this problem by checking the options one by one. The first function is sinx. We know that sinx is not a one-one function. Because if we draw lines parallel to x-axis the lines would cut the graph more than once. So option A can’t be correct.

Let’s move to option B. The next function is f(x) = x. This function is a straight line function and we know that all the straight line functions( except the constant function y = k ) are one – one. So it’s a one –one function. Now let’s check whether the function is onto or not. The co-domain given for the function is R. We know that the range of the function is also R. So the range and codomain is equal and the function is onto.

This is our answer.

But we can check for other options as well and we’ll find that other two functions are not one-one onto. And the correct option is B.