Let $f: R \rightarrow R$ be defined by $f(x) = 2x + 6$,which is a bijective mapping. Then $f^{-1}(x)$ is given by:

Let $f(x)=(x+1)^2-1$ for $x \geq -1$.
Statement-$1$: $S=\{x:f(x)=f^{-1}(x)\}=\{0, -1\}$
Statement-$2$: $f$ is a bijection.

Let $f: R \rightarrow R$ be defined as $f(x)=10x+7$. Find the function $g: R \rightarrow R$ such that $g \circ f = f \circ g = I_{R}$.

If $f$ is the inverse function of $g$ and $g^{\prime}(x)=\frac{1}{1+x^n}$,then the value of $f^{\prime}(x)$ is

Let $f(x) = \sin x + \cos x$ and $g(x) = x^2 - 1$. Then $g(f(x))$ is invertible for $x \in $

Let $f: N \rightarrow Y$ be a function defined as $f(x) = 4x + 3$,where $Y = \{y \in N : y = 4x + 3\}$ for some $\{x \in N\}$. Show that $f$ is invertible. Find the inverse.