List of top Quantitative Aptitude Questions on Functions asked in NPAT

The range of the function \( f(x) = \sqrt{16 - x^2} \) is:
If \( f(x) = \frac{x-1}{x+1} \), then which of the following will be true?
Let \( A = \mathbb{R} - \{ 3 \} \) and \( B = \mathbb{R} - \{ 1 \} \). Let \( f : A \to B \) be defined by \( f(x) = \frac{x-2}{x-3} \). What is the value of \( f^{-1} \left( \frac{1}{2} \right) \)?
If function $f: \mathbb{R} \rightarrow \mathbb{R}$ is defined by $f(x) = 2x - 3$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ is defined by $g(x) = x^3 + 5$, then the value of $(f \circ g)^{-1}(-9)$ is:
If \( f\left(1 - \frac{1}{x} \right) = \frac{5x + 1}{x}, \, x \neq 0 \), then \( f(x) = k - x \). What is the value of \( k \)?
If \( f(x) = 4x^3 - 8 \), then what is the value of \( f^{-1}(-8) + f^{-1}(24) \)?
Let $A = \{2, 4, 6, 9\}$ and $B = \{4, 6, 18, 27, 81\}$. If $C = \{(x, y) \mid x \in A, y \in B$ such that $x$ is a factor of $y$ and $x<y\}$, then $n(C)$ is:
If \( f(2x) = \frac{2}{2 + x} \) for all \( x>0 \), and \( 5f(x) = 8 \), then what is the value of \( x \)?
Let \( f(x) = \frac{3x - 5}{2x + 1} \). If \( f^{-1}(x) = \frac{-x + a}{bx + c} \), then what is the value of \( (a - b + c) \)?
Given \( f(x) = \frac{-4x + 1}{4} \) and \( g(x) = \sqrt[3]{x} \), then \( (g \circ f^{-1})\left(\frac{3}{8}\right) = \)
If \( f(x) = \frac{x-1}{x+1} \), then for \( k>0 \), \( f^{-1} \left( \frac{1}{2k+3} \right) = ?
Which of the following functions satisfies these two criteria: \( f(0) = 0 \) and \( f(x+1) = 2f(x) + 1 \)?
If \( f(x) = \frac{1}{x^2 + 1} \), \( 0<x<1 \), then \( f^{-1} \left( \frac{1}{4} \right) + f^{-1} \left( \frac{3}{4} \right) \)= : ?
If \( f(x) = \frac{x-1}{x+1} \), then for \( k>0 \), \( f^{-1} \left( \frac{1}{2k+3} \right) = ?
Which of the following functions satisfies these two criteria: \( f(0) = 0 \) and \( f(x+1) = 2f(x) + 1 \)?
If \( f(x) = \frac{1}{x^2 + 1} \), \( 0<x<1 \), then \( f^{-1} \left( \frac{1}{4} \right) + f^{-1} \left( \frac{3}{4} \right) \)= : ?
If \( f(2x) = \frac{2}{2 + x} \) for all \( x>0 \), and \( 5f(x) = 8 \), then what is the value of \( x \)?
Let \( f(x) = \frac{3x - 5}{2x + 1} \). If \( f^{-1}(x) = \frac{x + a}{bx + c} \), then what is the value of \( (a - b + c) \)?
Given \( f(x) = \frac{4x + 1}{4} \) and \( g(x) = \sqrt{x^3} \), then \( (g \circ f^{-1}) \left( \frac{3}{8} \right) = \)?