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