Investigation 8 1 Consider the function f(x) = 2x+4. a Explain why fhas an inverse function f-1. b Complete the table for fand f-1. (x, f(x)) lies on the graph of f YL→X= f'v) v.fv) lies on the graph of f-1 y=f(x) xL»y = f(x) -4 A(-4,_) A'(-,-4) -2 B(_,-2) B'(-2,-) C(-,0) C'(0,-) D(0,_) D'(_,0) E(1, 6) 6 →1 E'(6, 1) 6. F(3,_) F'(-,3) c The points E and E' have already been plotted on the given set of axes. i Draw the graph of f(x) = 2x+4. 10 Also, clearly plot and label the other five points on the graph of fthat were found in part b. 6 ii Plot and label the other five points on the graph of f-1 that were found in part b. 4 2 d What can you say about the type of graph f-1 is? How would you find more points on this graph? Write down at least three more points on the graph -10 -8 of f-1, then complete the graph of f-. e What can you say about the position of the point B'with respect to the position of the point B? And what about the position of C' with respect to C? f There is one point that lies on both graphs. What is it? What do you notice about the coordinates of this point? -6 -4 -2 -2 2 4 8 10 -6 -8 -10 This point also lies on the line that bisects the first and third quadrants, the identity line. What is the equation of this line? Draw it with a dotted line on the set of axes. How would you describe the positions of the graphs of fand f-l with respect to the identity line? g Now explain how you would draw the graph of f1 if you are given the graph of f. h What is the equation of the inverse functionf-1? 4. 1. 3.

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.