Q57 / 150 · MHT CET 2026 (13 April Shift 2) · Mathematics
If $g(x)$ is the inverse function of $f(x)$, where $f(x) = \dfrac{5x+3}{4x-1}$, then $g(1) =$
- Correct answerA$-4$
- B$\dfrac{-1}{4}$
- C$\dfrac{8}{3}$
- D$\dfrac{3}{8}$
Solution
Given $f(x) = \dfrac{5x+3}{4x-1}$ and $g(x)$ is the inverse function of $f(x)$.
By definition of inverse functions, if $g(1) = x$, then $f(x) = 1$.
Substituting $f(x) = 1$ into the given function:
$\dfrac{5x+3}{4x-1} = 1$
$5x + 3 = 4x - 1$
$5x - 4x = -1 - 3$
$x = -4$
Therefore, $g(1) = -4$.
Answer: $-4$
By definition of inverse functions, if $g(1) = x$, then $f(x) = 1$.
Substituting $f(x) = 1$ into the given function:
$\dfrac{5x+3}{4x-1} = 1$
$5x + 3 = 4x - 1$
$5x - 4x = -1 - 3$
$x = -4$
Therefore, $g(1) = -4$.
Answer: $-4$
Hence, the correct answer is option: 'A'.