List of top Mathematics Questions on Functions asked in MHT CET

If \( f(x) = 3x + 6 \), \( g(x) = 4x + k \), and \( f \circ g(x) = g \circ f(x) \), then find \( k \):

Range of the function $f(x) = 3 + 2^x + 4^x$ is

The domain of the function $\log_{10}(x^2 - 5x + 6)$ is

If $f(x) = 3[x] + 5\{x + 1\}$, where $[x]$ is greatest integer function of $x$ and $\{x\}$ is fractional part function of $x$, then $f(-1.32) =$

Let \( A = \{10, 11, 12, 14, 26\} \) and let \( f : A \to \mathbb{N} \) be such that \( f(a) = \) highest prime factor of \( a \), where \( a \in A \), then range of \( f = \)

The domain of the function $f(x) = \frac{1}{\sqrt{x + |x|}}$ is

If $f(x) = 3[x] + 5\{x + 1\}$, where $[x]$ is greatest integer function of $x$ and $\{x\}$ is fractional part function of $x$, then $f(-1.32) =$

If \( f(x)=\dfrac{4x+7}{7x-4} \), then the value of \[ f\{f[f(2)]\} \] is

The domain of the real valued function \[ f(x) = \frac{x + 2}{9 - x^2} \] is

If $f:\mathbb{R}\rightarrow\mathbb{R}$ is given by $f(x)=7x+8$ and $f^{-1}(12)=\dfrac{k}{7}$, then the value of $k$ is

If \( f : \mathbb{R} \rightarrow \mathbb{R} \) such that \[ f(x) = \frac{e^{x} + e^{-x}}{e^{x} - e^{-x}}, \] then \( f \) is

If \( f : \mathbb{R} \to \mathbb{R}, g : \mathbb{R} \to \mathbb{R} \) are defined by \[ f(x) = x^2 - 3x + 4 \quad \text{and} \quad g(x) = 2x + 1, \quad \text{then the value of} \quad x \text{ for which} \quad f(x) = f \circ g(x) \text{ is} \]

If \[ f(x) = \begin{cases} 6\beta - 3x, & \text{if } -4 \leq x<-2,
4x + 1, & \text{if } -2 \leq x \leq 2, \end{cases} \] is continuous on \( [-4, 2] \), then \( \alpha + \beta = \)

If \( f : \mathbb{R} \rightarrow \mathbb{R} \), \( g : \mathbb{R} \rightarrow \mathbb{R} \) are two functions defined by \( f(x) = 2x - 3 \), \( g(x) = x^3 + 5 \), then find \( (f \circ g)^{-1(x) \).}

If $f : R - \{2\} \to R$ is a function defined by $f(x) = \frac{x^2 - 4}{x - 2}$ , then its range is

Find the function $ f(x_1, x_2, x_3) $ satisfying $ f(x_1, x_2, x_3) = 1 $ at $ x_1 = 1, x_2 = x_3 = 0 $ .