Question 139

Let $$f: R \rightarrow R$$ be a function defined by $$f(x) = 2x^3 + 8$$ for all $$x \epsilon R$$, then the function f is

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Solution:

The graph will be similar to that of $$x^3$$, just displaced 8 units upwards.

As, a function is a one-to-one function when it will pass the vertical line test (to make it a function) and also a horizontal line test (to make it one-to-one).

So it is one-one.

Also,

Also, as you progress along the line, every possible y-value is used.So it is also Onto.

Hence it is bijection.

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