Functions Test ...

$$f:R\rightarrow R , g:R\rightarrow R$$ and  $$f(x)= \sin x$$, $$g(x)=x^{2}$$ then $$fog(x)=$$

Find the value of $$\displaystyle \left( g\circ f \right) \left( 6 \right) $$ if $$\displaystyle g\left( x \right) ={ x }^{ 2 }+\frac { 5 }{ 2 } $$ and $$\displaystyle f\left( x \right) =\frac { x }{ 4 } -1$$.

If $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ are defined by $$f(x) =3x -4$$, and  $$g(x)=2 + 3x$$, find $$(g^{-1}\, of^{-1})(5)$$.

If $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ are defined by $$f(x) =2x +3, g(x)=x^2 + 7$$, what are the values of $$x$$ such that $$g(f(x))=8$$?

If $$f(x) = \sqrt {x^{2} - 3x + 6}$$ and $$g(x) = \dfrac {156}{x +17}$$, find the value of the composite function $$g(f(4))$$.

Find the correct expression for $$\displaystyle f\left( g\left( x \right)  \right) $$ given that $$\displaystyle f\left( x \right) =4x+1$$ and $$\displaystyle g\left( x \right) ={ x }^{ 2 }-2$$

For what value of x is $$fog = gof$$ if $$f(x)=x - 2$$ and $$g(x)=x^3+3$$?

Which of the following functions is/are constant ?

Let $$f:\mathbb{R}\rightarrow \mathbb{R}$$ be a function such that for any irrational number $$r,$$ and any real number $$x$$ we have $$f(x)=f(x+r)$$. Then, $$f$$ is

If $$f: A \rightarrow B$$ is a bijective function and if n(A) = 5, then n(B) is equal to