I
verb
1
BAD : I don't go swimming because I fear of the water.
GOOD : I don't go swimming because I am afraid of the water.
GOOD : I don't go swimming because of my fear of the water.
BAD : He fears to lose his job.
GOOD : He is afraid of losing his job.
GOOD : His fear is that he may lose his job.
GOOD : He fears that he may lose his job.
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Fear is used mainly as a noun: 'My worst fear is that I won't be able to have children.' 'The whole of his life has been dominated by fear of failure.'
As a verb, fear is used mainly in formal styles to mean 'be frightened about what may happen if you do something': 'Government officials fear that if they put up taxes, they may lose the election.' 'The rescuers feared that the remains of the building might collapse on top of them.'
2
BAD : All these problems make me fear about the children's future.
GOOD : All these problems make me fear for the children's future.
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fear for = be worried about the safety or well-being of someone: 'The parents of the kidnapped child did not inform the police because they feared for her safety.'
II
noun
1
BAD : Then I heard the voice again and I had fear.
GOOD : Then I heard the voice again and I was afraid.
BAD : I had fear of being alone.
GOOD : I was afraid of being alone.
BAD : She suddenly felt fear.
GOOD : She suddenly felt afraid.
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be/feel afraid/frightened/scared (NOT feel/have fear ): 'Don't be afraid. The dog won't hurt you.' 'There's nothing to be scared of.'
Compare: have a fear of sth (= be afraid of something for a long time or all your life): 'I've always had a fear of heights.'
2
BAD : It took me a long time to overcome my fear to fly.
GOOD : It took me a long time to overcome my fear of flying.
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fear of (doing) sth : 'I have never been able to get over my fear of heights.'