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# Solving Literal Equations

## 6.3 Families of Functions and Solving Literal Equations

#### Families of Functions and Solving Literal Equations

• For instance, y=2 x^{3},\ y=-\frac{1}{4} x^{3} can all belong to a family function f(x)=k x^{3},\ k \neq 0.
• Functions from the same family would exhibit some similarities. Apart from the general shape of its graph, they might share some other things, such as a same intercept, a same asymptote, and so on.
• Literal equations can also be applied on the 3 types of functions we learnt for various things; it is simply a combination of all the knowledges you have learnt.

Example

Let f: R \rightarrow R, and f(x)=m x+2 where m \in R^{+}. Find: a) Its x-intercept; b) The values of m where its x-intercept is lesser than 2; c) Its inverse function; d) The equation of the line perpendicular to f(x) at (0,\ 2).

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## 6.2 Literal Equation Systems: Polynomials

#### Solving Literal Equations: Polynomials

• Simply put, you just need to treat all pronumerals as numbers. Then, use your knowledge with polynomials to solve them.

Example

Solve the following:

a) x^{2}+k x+k=0;

Using our knowledge of solution for quadratic functions, we know that

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## 6.1 Revision for Linear Systems

#### Linear Literal Equation Systems

• In previous years, you are already equipped with the skills to solve simple linear equations like 4 y-\frac{(3 y+4)}{2}+\frac{1}{3}=\frac{5(4-y)}{3}, including their corresponding worded problems. The skills learnt are crucial and will be applied in the topics explored in this course.
• A literal equation in x is an equation whose solution will be expressed in terms of pronumerals rather than numbers.

In simpler terms, instead of solving

2x+5=7

instead you will be dealing with

ax+b=c

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