Inverse Equations Problem "A" Is an Example Essay

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Inverse Equations

Problem "a" is an example of substitution equations. In this case, it is asking the two equations to be subtracted and the number four substituted for "x." In order for this operation to be properly accomplished, order of operations requires that the two problems be simplified to their final state before being combined.

Proof a.

(f-h)(4)

Problems "b" are examples of inverse functions. Here, a secondary function is being placed in the original function's "x" position. Once this is accomplished, order of operations and rules of simplification allow for the simplifying of the final expression. These cannot be entirely solved as there is no value given for "x."

Proof b.

2(x^2 -- 3) +

2x^2 -- 6 +

2x^2 -- 1

(7 -- (x^2 -- 3)) /

(7 -- x^2 + 3) /

(10 -- x^2) /

Problems "c" are examples of finding the inverse of a single function.

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According to inverse theory, this can be accomplished by substituting "y" for "f (x)" and then solving for x. All common rules of algebra must be applied during the solving resulting in the inverse equation.

Proof c.

f (x) = 2x + 5

y = 2x + 5

y -- 5 = 2x

(y -- 5) / 2 = x f (x)^-1= (x -- 5)/2

h (x) = (7 -- x)/3

y= (7 -- x)/3

3y= 7 -- x

3y -- 7 = -x h (x)^-1 = -3x + 7

As with anything in mathematics, linear….....

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