Question The function g is defined by for . By first completing the square, find an expression for and state the domain of . Solution We are given that; We use method of “completing square” to obtain the desired form. We complete the square for the terms which involve . We have the algebraic formula; […]
Question Functions f and g are defined by; for for Where is a constant. i. Find the value of for which the line is a tangent to the curve . ii. In the case where , find the set of values of for which . iii. In the case where , […]
Question a) Given that x > 0, find the two smallest values of x, in radians, for which . Show all necessary working. b) The function is defined for . i. Express f(x) in the form , where a and b are constants. ii. Find the range of f. Solution a) We […]
Question The functions f and g are defined by for for . i. Find the range of f and the range of g. ii. Find an expression for fg(x), giving your answer in the form , where a, b and c are integers. iii. Find an expression for , giving your answer in the […]
Question The function f is defined by for . The function g is defined by for where and are constants. i. Find the greatest value of and the least value of which will permit the formation of the composite function gf. It is now given that the conditions for the formation of gf are satisfied. […]
Question The functions f and g are defined by , , i.Obtain expressions for and , stating the value of x for which is not defined. ii.Solve the equation Solution i. We are given; for for We have; We write them as; To find the inverse of a given function we need to write it […]
Question The functions f is defined by for , i. State the range of . ii. Sketch the graph of . The functions g is defined by for , where is a constant. iii. State the largest value of for which g has an inverse. iv. For this value of , find an […]
Question The function f is defined by for . i. Express in the form of where and are constants. ii. State the greatest value of . The function g is defined by for . iii. Find the value of for which . Solution i. We have the expression; We use […]
Question i. Express in the form of . The function f is defined by for , where is constant. ii. State the largest value of for which is a decreasing function. The value of is now given to be 1. iii. Find an expression for and state the domain of . iv. The […]