Functions questions | form five Pure Advanced Mathematics

Find Functions examination questions, form five Pure Advanced Mathematics in acaproso.com

#	Question
1	For the function, f(x) =^[ ^(x+1)(x+3)]/_[x²+8x+12] sketch the curve of the function Find its domain and range Mathematical Calculation
2	The function fis defined by f(x) = ⁽^3x-2)/_(x+1) what is the range of f find f^-1(x) determine the domain and range of f^-1(x) Mathematical Calculation
3	Given that f(x)=10x, g(x)=x+3 find fg(x) and (fg)^-1 (x). Verify that if b=fg(a) then (fg)^-1(b)=a. Find the set of values of p for which $f(x)=x^2+3px+p$ is greater than zero for all real values of x. Mathematical Calculation
4	Given the functions $f(t)=e^{t}$ and $g(t)=ln t$ . Show that $fcirc g(t)=gcirc f(t)$ . If $f(t)=at$ , $g(t)=bt^{2}+3$ , $(fcirc g)(2)=35$ and $(fcirc g)(3)=75$ , find the values of a and b. Mathematical Calculation
5	Given that , $f(x)=frac{x^{3}}{1-x^{2}}$ find horizontal and vertical asymptotes of f(x). Sketch the graph of f(x). State the domain and range of the function f(x). Mathematical Calculation
6	Draw the graph of $f(x)=x^{3}-3x^{2}-6x+8$ in the interval [-5,6]. Hence tell how $f(x)$ behaves for positively and negatively large values of x. Mathematical Calculation
7	Find $fcirc g(x)$ given that $f(x)=2x^{2}+1$ and $g(x)=frac{4x}{x^{2}-2}$ , hence Determine the vertical and horizontal asymptotes of $f circ g(x)$ . Draw the graph of $f circ g(x)$ . State the domain and range of $f circ g(x)$ . Mathematical Calculation
8	Given that $f(x)=2^{x}$ and $g(x)=log_{2}x$ , find the domain and range of f(x) and g(x). draw the graphs of f(x) and g(x) on the same axes. Comment on the resulting graphs. Mathematical Calculation
9	Given that $f(x)=frac{2x-x^{2}}{x^{2}-2x-3}$ , write the values of x for which f(x)=0 and the values of x for which f(x)>0. show that $f(x) ightarrow -1$ as $x ightarrow pm infty$ . sketch the grap of f(x), showing particularly where the curve crosses the x-axis and how it approaches its asymptotes. Mathematical Calculation
10	If $f(x)=sqrt{x^{2}-9}$ and $g(x)=x-2$ , find $f(g(x))$ . Draw the graph of $f(g(x))$ obtained in part (a) above. Mathematical Calculation