Relations and F...

Find $$g(x)$$, if $$f(x) = 5x^{2} + 4$$ and $$f(g(3)) = 84$$

If the binary operation $$a$$ # $$b = a^{b} - \sqrt {b}$$, then $$(2$$ # $$4) - (4$$ # $$2) =$$

If $$h(x) = x^2, g(x)= x^2 -3$$ and f(x)= x -2, what can you say about ho(gof) and (hog)of?

Which of the following functions are not identical?

The function $$f(x)={x}^{2}+bx+c$$, where $$b$$ and $$c$$ real constants, describes

If f(x)=x+2and $$g(x)=x^2-3$$, then which is true?

Given $$g(x)=9\log_8(x-3)-5, g^{-1}(13)=$$

If $$f(x) = 4x^{2} - 1$$ and $$g(x) = 8x + 7, g\circ f(2) =$$

Let $$f:\{x, y , z\} \rightarrow \{1, 2, 3\}$$ be a one-one mapping such that only one of the following three statements and remaining two are false : $$f(x) \neq 2, f(y) =2, f(z) \neq 1$$, then 

$$f(x)=x^2-x+5$$ and $$g(x) = f^{-1}(x)$$. Then $$g'(7)=$$