Composition of function: Conditions and Properties - Practice Questions & MCQ

Let $f(x)=2^{10} \cdot x+1 \text { and } g(x)=3^{10} \cdot x-1 \text {. If }(f \circ g)(x)=x$, then x is equal to:

If $\mathrm{f}(\mathrm{x})=\frac{4 \mathrm{x}+3}{6 \mathrm{x}-4}, \mathrm{x} \neq \frac{2}{3}$ and (fof) (x) $\mathrm{g}(\mathrm{x})$, where $\mathrm{g}: \mathbb{R}-\left\{\frac{2}{3}\right\} \rightarrow \mathbb{R}-\left\{\frac{2}{3}\right\}$, then (gogog)(4) is equal to

For $\mathrm{f}(\mathrm{x})$ and $\mathrm{g}(\mathrm{x})$, find the calculation for which $\mathrm{fog}(\mathrm{x})$ can be evaluated.

Identify the correct statement:

If $(1,2) \in S o R, \mathrm{~S} \& \mathrm{R}$ are 2 relations from B to C and A to B respectively, then there exists $b \in B$, such that:

If $f(x)=\frac{1}{\sqrt{x}}, g(x)=x-2$, then the domain of $f \circ g(x)$ is

If $f=\{(1,2),(3,4),(5,6)\}$ and $g=\{(2,4),(3,5),(4,1)\}$, then the value of $f \circ g(3)+g \circ f(1)$ is

If P is the number of prime numbers less than or equal to 52, and q is the numbers composite numbers less than or equal to 52, then p + q equals