Question The functions f and g are defined by for for i. Find an expression for . ii. Solve the equation . Solution i. We are given the function; We write it as; To find the inverse of a given function we need to write it in terms of rather than in terms of . As demonstrated in (i), […]
Question a. The function f, defined by for , is such that and . i. Find the values of the constants a and b. ii. Evaluate . b. The function g is defined by for for . The range of g is given by . Find the values of the constants c and d. Solution a. i. We are given the […]
Question A function f is defined by for . i. Find an expression for and find the point of intersection of the graphs of and . ii. Sketch, on the same diagram, the graphs of and , making clear the relationship between the graphs. Solution i. We have; We write it as; To find the inverse of a given […]
Question Functions f and g are defined for x > 3 by; i. Find and simplify an expression for gg(x). ii. Find an expression for and state the domain of . iii. Solve the equation . Solution i. We are given that; It can be written as; Therefore for ; ii. We […]
Question A function f is defined by for . It is given that f is an increasing function. Find the largest possible value of the constant a. Solution We are given that function f is increasing function. To test whether a function is increasing or decreasing at a particular point , we take derivative of a function at that […]
Question The function f is defined by , for . i. Solve the equation , giving your answer correct to 1 decimal place. ii. Find an expression for and find the domain of . iii. Sketch, on the same diagram, the graphs of y=f(x) and . Solution i. We are given the function as; We are required to […]
Question The functions f and g are defined for by i. Show that and obtain an unsimplified expression for . ii. Find an expression for and determine the domain of . iii. Solve the equation . Solution i. We are given the functions; We can rewrite these as; First we find . Next we find . ii. […]
Question The function f is defined by for , . i. Find an expression for . The function g is defined by for , where a is a constant. ii. Find the value of a for which . iii. Find the possible values of a given that the equation has two equal roots. Solution i. We […]
Question The equation of a curve is . i. Sketch the graph of for , stating the coordinates of the point of intersection with the y-axis. Points P and Q lie on the curve and have x-coordinates of and respectively. ii. Find the length of PQ correct to 1 decimal place. The line through P and […]
Question i. Express in the form , where a, b and c are constants. The function is defined by for , where p is a constant. ii. State the smallest value of for which is a one-one function. iii. For this value of , obtain an expression for , and state the domain of . iv. State the set of values of for […]