Question:
If \(g(x)\) is the inverse function of \(f(x)\), where \(f(x) = \frac{5x+3}{4x-1}\), then \(g(1) =\)
If \(g(x)\) is the inverse function of \(f(x)\), where \(f(x) = \frac{5x+3}{4x-1}\), then \(g(1) =\)
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\(g(1)\) is the number \(x\) for which \(f(x) = 1\).
Updated On: Oct 1, 2026
- \(-4\)
- \(\frac{-1}{4}\)
- \(\frac{8}{3}\)
- \(\frac{3}{8}\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
If \(g\) is the inverse of \(f\), then \(g(1) = a\) means \(f(a) = 1\). So we solve \(f(x) = 1\).
Step 2: Solve:
\[ \frac{5x+3}{4x-1} = 1 \Rightarrow 5x + 3 = 4x - 1 \Rightarrow x = -4 \]
Check: \(f(-4) = \frac{-20+3}{-16-1} = \frac{-17}{-17} = 1\).
Final Answer:
\(g(1) = -4\), option (A). \[ \boxed{-4} \]
If \(g\) is the inverse of \(f\), then \(g(1) = a\) means \(f(a) = 1\). So we solve \(f(x) = 1\).
Step 2: Solve:
\[ \frac{5x+3}{4x-1} = 1 \Rightarrow 5x + 3 = 4x - 1 \Rightarrow x = -4 \]
Check: \(f(-4) = \frac{-20+3}{-16-1} = \frac{-17}{-17} = 1\).
Final Answer:
\(g(1) = -4\), option (A). \[ \boxed{-4} \]
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