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IB Mathematics - Chapter 1 Worked Examples III

Functions

· IB,Mathematics,ib mathematics,domain,functions

Example 9

Given f(x)=3x+5 and g(x)=2(1-x)

a) find f^-1(2)

b) find (gof)(-4)

Answer

a) f(x)=3x+5

     y=3x+5

     x=3y+5

     y=(x-5)/3

     f^-1(2)=(2-5)/3

     f^-1(2)=-3/3=1

 

b) f(-4)=3(-4)+5

    f(-4)=-7

    (gof)(-4)=2(1--7)

    (gof)(-4)=16

Example 10

How can you check whether a function has an inverse?

Answer

Use the horizontal line test- if it has an inverse then it will not cross a horixontal line more than once.

Example 11

In what line is a function reflected in to create its inverse?

Answer

y=x

Example 12

If f(x)=3x-2 find the inverse function f^-1(x) in IB Mathematics

Answer

y = 3x-2

x=3y-2

3y=x+2

y=(x+2)/3

f^-1(x)=(x+2)/3

Example 13

Given the graph of a function is f(x), how would it be translated according to IB Mathematics curriculum if it became:

a) f(x+1)

b) f(x)-2

c) f(-x)

d)-f(x)

e) 2f(x)

Answers

a) translated one unit to the left

b) translated two units down

c) reflected in the y axis

d) reflected in the x axis

e) vertically stretched by a scale factor of 2

End of topic!

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IB Mathematics - Chapter 1 Worked Examples II
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I/GCSE Physics: Forces in Motion
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