Question i. The diagram shows part of the curve and part of the straight line meeting at the point , where and are positive constants. Find the values of and . ii. The function f is defined for the domain by Express in a similar way. Solution i. It is evident from the diagram that […]
Question The function is such that , for . i. Find the coordinates and the nature of the stationary point on the curve . The function g is such that , , where is a constant. ii. State the smallest value of for which has an inverse. For this value of k, iii. Find an expression for . iv. Sketch, on […]
Question Functions and are defined by for for , i. Obtain expressions, in terms of , for and , stating the value of for which is not defined. ii. Sketch the graphs of and on the same diagram, making clear the relationship between the two graphs. iii. Given that the equation , where is a constant, has no solutions, find the set of […]
Question It is given that a curve has equation , where . i. Find the set of values of for which the gradient of the curve is less than 5. ii. Find the values of at the two stationary points on the curve and determine the nature of each stationary point. Solution i. Gradient (slope) of the curve is […]
Question The functions and are defined for by Solve the following equations for . i. , giving your answer in terms of . ii. , giving your answers correct to 2 decimal places. Solution i. We have the functions; We write as; We are given that; Therefore; ii. We have the functions; We write as; We are given that; Therefore; We utilize the […]
Question The function is such that for . Find i. in the form where , and are constants, ii. the domain of . Solution i. We have the functions; for 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 . Interchanging ‘x’ with ‘y’; ii. […]
Question The function is defined by for . i. Express in the form , and hence state the coordinates of the vertex of the graph of . The function is defined by , for . ii. State the range of . iii. Find an expression for and state the domain of . Solution i. We have the function; We have the expression; […]
Question The function is defined for the domain , where and are constants. i. Express in the form , where and are constants. ii. State the range of in terms of . iii. State the smallest value of for which is one-one. iv. For the value of found in part (iii), find an expression for and state the domain of , giving your answers […]