The function f f\,f is defined by
f:x↦ln(4−2x),x<2 and x∈R. f : x \mapsto \ln(4 - 2x), \quad x < 2 \text{ and } x \in \mathbb{R}. f:x↦ln(4−2x),x<2 and x∈R.Show that the inverse function of f f\,f is defined by
f−1:x↦2−12ex f^{-1} : x \mapsto 2 - \frac{1}{2} e^x f−1:x↦2−21exand write down the domain of f−1f^{-1}f−1.
Write down the range of f−1f^{-1}f−1.
Sketch the graph of y=f−1(x)y = f^{-1}(x)y=f−1(x). State the coordinates of the points of intersection with the x x\,x and y y\,y axes.
The graph of y=x+2y = x + 2y=x+2 crosses the graph of y=f−1(x)y = f^{-1}(x)y=f−1(x) at x=kx = kx=k. The iterative formula xn+1=−12exn,x0=−0.3,\displaystyle x_{n+1} = -\frac{1}{2} e^{x_n}, x_0 = -0.3,xn+1=−21exn,x0=−0.3, is used to find an approximate value for kkk. Calculate the values of x1 x_1\,x1 and x2x_2x2, giving your answer to 4 decimal places.
Find the values of k k\,k to 3 decimal places.
7 exam-style questions on Edexcel A Level Old Maths Numerical Methods. Each one has a worked solution and a mark scheme showing where the marks go.