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Consider the function
f(x) =1/2 (2x +2-x)
which has the graph
(a) Explain why f has no inverse function. You should include an example to support your explanation.
(b) Determine the largest possible domain, which includes x = 1, for f(x) such that the inverse function f-1(x) does exist.
(c) Given your answers in (b) find the inverse function f-1(x). Clearly explain key steps and show all working.
(d) Sketch the graph of y = f(x) for the restricted domain in (b) and y = f-1(x) on the same set of axes. All points of intersection and axes-intercepts should be easily determined from your sketch or clearly labelled. Furthermore axes should be clearly labelled with appropriate scaling. It is suggested you use different colours for the two graphs and clearly label each graph.
Horizontal tangents for Parametric Equations Horizontal tangents will take place where the derivative is zero and meaning of this is that we'll get horizontal tangent at value
inverse rule of x3-5
how do mathematical ideas grow?
3 items x, y and z will have 6 different permutations however only one combination. The given formular is generally used to determine the number of combinations in a described situ
There are 81 women teachers at Russell High. If 45% of the teachers in the school are women, how many teachers are there at Russell High? Use the proportion part/whole = %/100.
x+2y^2=63 and 4x+y^2=0; Find the area of the regions enclosed by the lines and curves.
(3x+2)^2 d^2y/dx^2+3(3x+2)dy/dx-36y=3x^2+4x+1
The curve (y+1) 2 =x 2 passes by the points (1, 0) and (- 1, 0). Does Rolle's Theorem clarify the conclusion that dy dx vanishes for some value of x in the interval -1≤x≤1?
4x+3y+7=0 and 3x+4y+8=0 find the regression coefficient between bxy and byx.
By using n = 4 and all three rules to approximate the value of the following integral. Solution Very firstly, for reference purposes, Maple provides the following valu
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