Her mother, Téa Leoni, expressed reservations based on her own experiences working as a woman in Hollywood.
"My mom definitely was trepidatious. She grew up in the industry; that was very difficult for women.
That we are now talking about more and changing, slowly but surely, and I'm her daughter, and she was scared for me to enter that world," West said.
Despite her initial worries, West recalled that her father altered his stance after watching her perform on stage.
"My dad has now admitted that before he was so nervous for me, and then he saw the play and he was like, 'oh, thank God, she's good.'
So I think that's kind of where he was at, at least," she said.
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West Duchovny has since built a resume with roles in A Mouthful of Air, Linoleum, Saint X, Painkiller, and the final episode of The X-Files.