The graphs given alongside represent two functions \(f(x)\) and \(g(x)\) respectively. Which of the following is true?
The graphs given alongside represent two functions \(f(x)\) and \(g(x)\) respectively. Which of the following is true?
Show Hint
- \(g(x) = |f(x)|\)
- \(f(x) = |g(x)|\)
- \(g(x) = -|f(x)|\)
- None of these
The Correct Option is C
Solution and Explanation
Step 1: Analyze the graphs
From the left graph (for \(f(x)\)):
Looks like a “V”-shaped graph opening upward → Suggests \(f(x) = |x|\) From the right graph (for \(g(x)\)):
“V”-shaped graph opening downward → Suggests \(g(x) = -|x|\)
Step 2: Compare definitions If \(f(x) = |x|\), then clearly: \[ g(x) = -|x| = -|f(x)| \Rightarrow g(x) = -|f(x)| \] % Final Answer: (c)
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