**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!

Drafted by Gina