$f: R \rightarrow R, f(x) = 3x + 2$ and $g: R \rightarrow R, g(x) = 6x + 5$. Find the value of $(g \circ f^{-1})(10)$.

The inverse of $y = 5^{\log x}$ is

Suppose $f(x)=(x+1)^{2}$ for $x \geq -1$. If $g(x)$ is a function whose graph is the reflection of the graph of $f(x)$ in the line $y=x$,then $g(x) = $

Let $f:(0,1) \rightarrow R$ be defined by $f(x)=\frac{b-x}{1-b x},$ where $b$ is a constant such that $0 < b < 1$. Then

If $y = f(x) = \frac{x + 2}{x - 1}$,then $x = $

Let $f: A \rightarrow B$ and $g: B \rightarrow A$ be defined as $f(x)=x^2 \forall x \in A$ and $g(x)=x^{1/2} \forall x \in B$. $f(x)$ and $g(x)$ are inverse functions to each other when