Relations and F...

$$f  : R \rightarrow R$$ is a function defined by $$f(x)=10x-7$$. If $$g=f^{-1}$$ then $$g(x) = $$

If $$f(x) = \dfrac{2x+5}{x^{2} + x + 5}$$, then $$f\left [ f(- 1 ) \right ]$$ is equal to

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

If $$ABC\sim PQR$$, then AB:PQ =

If $$f$$ and $$g$$ are one-one functions from $$R\to R$$, then

If $$f :  R^+ \rightarrow R$$ such that $$f(x) = \log_3 x$$ then $$f^{-1}(x) = $$

Which of the following functions are one-one?

A mapping function $$f:X\rightarrow Y$$ is one-one, if

Let $$\displaystyle f:R\rightarrow A=\left \{ y: 0\leq y< \dfrac{\pi}{2} \right \}$$ be a function such that $$\displaystyle f(x)=\tan^{-1}(x^{2}+x+k),$$ where $$k$$ is a constant. The value of $$k$$ for which $$f$$ is an onto function is 

If $$f:R\rightarrow R$$ given by $$f(x)={ x }^{ 3 }+({ a+2)x }^{ 2 }+3ax+5$$ is one-one, then $$a$$ belongs to the interval