[tex]\boxed{\boxed{\pink{\sf Yes \ it\ is \ one\ to \ one \ function .}}}[/tex]
A function is said to be be one-to-one ( injective) if every y-value has only one corresponding x-value. The given function is ,
[tex]\bf \implies f(x) = 2x^3-5\\\\\bf\implies y = 2x^3-5 [/tex]
Here I have made the graph of " Desoms Graphing calculator. "
Now ,on plotting its graph we see that every y-value has only one corresponding x-value . Hence , ihe given function is a injective function that is one to one function.