if/whether

"If" as a synonym for "whether" is commonly used with words like "doubt," "see," "ask," "wonder," "decide," and "know." After "determine," "deliberate," or "reconsider," etc., "whether" is the natural choice. That is, the choice should be determined by considerations of collocation and register, not by an arbitrary (and false) rule that "if" must never be tolerated in such clauses and should only be used in its conditional ("if. . .then") sense.

There are times when "if" is not a proper synonym for "whether." Examples:
Let me know whether you want cake.
Let me know if you want cake.

In these examples, the grammatically correct word would depend on the intended meaning. The difference is this: The first example means "Whether you want cake or you don"t want cake, let me know," whereas the second example means "If you want cake, (then) let me know." There is a difference.

Evans 1957 says that the notion that "if" may not introduce a noun clause, as "whether" may, is a recent one, but it can be traced back to an 18th century dictionary editor. More recent American commentators find the usage of "if" to mean "whether" standard and find "whether" more often used informal contexts. The notion that "whether" and not "if" should be used to introduce a clause is still open to debate.

Merriam Webster"s Dictionary of English Usage has a rather lengthy discussion on this issue, noting that most twentieth-century commentators find the usage of "if" to introduce a clause standard, but adding that "whether" is used in more formal contexts.

The "whether" sense of "if" is not used at the beginning of a sentence. The initial "if" is understood as the ordinary conditional use. The "whether" sense is rarely found except after a verb, and sometimes after adjectives. The insistence on "whether" when an alternative is specified is called "superstition" by Copperud (a noted usage expert).

There is quite a bit more regarding the subjunctive us of "if." Basically, the subjunctive "if" should be used when a clause contains a condition that is hypothetical or contrary to fact, which is sometimes a subjective judgment.

grammarNOW! says:
The use of "or not" (with "whether") is redundant. It is implied in "whether" and should be omitted.