Question i. Express in the form , where a, b and c are constants. ii. Functions f and g are both defined for . It is given that and . Find . iii. Find and give the domain of . Solution i. We have the expression; We use method of “completing square” […]
Question A function f is defined by for . i. Find the range of f. ii. Sketch the graph of iii. Solve the equation , giving answers in terms of . The function is defined by for , where k is a constant. iv. State the largest value of k for which g has an inverse. v. For this value of k, find […]
Question The functions f and g are defined by for for . i. Find and simplify an expression for and state the range of . ii. Find an expression for and find the domain of . Solution i. We are given; for for . We are required to find expression for ; We are also […]
Question The function f is such that for . The function g is such that for , where a, b and q are constants. The function fg is such that for . i. Find the values of a and b. ii. Find the greatest possible value of q. It is now given that . iii. Find the range of fg. iv. Find […]
Question The function is defined by for . i. Find the set of values of x for which f(x) ≤ 3. ii. Given that the line y=mx+c is a tangent to the curve y = f(x), show that The function g is defined by for x ≥ k, where k is a constant. iii. Express in the form , where a […]
Question Functions and are defined by , ,, Solve the equation Solution First we find left hand side of required equation . We are given; It can be written as; Therefore; Now we find right hand side of required equation . We are given; These can be written as; Therefore; Now for substitute ; Finally, equating left […]
Question The function is defined by for . i. State the range of . ii. Find the coordinates of the points at which the curve intersects the coordinate axes. iii. Sketch the graph of . iv. Obtain an expression for , stating both the domain and range of . Solution i. […]
Question The function is such that for , where a and b are constants. i. For the case where and , find the possible values of a and b. ii. For the case where and , find an expression for and give the domain of . Solution i. We are given that function is represented as; We are given that; First we substitute […]