Example 5
a) Evaluate the function f(x)=2x+1 at x=3 in IB Mathematics
b) If f(x) =x^2+4x-3, find i) f(2), ii) f(0), iii) f(-3), iv f(x+1)
Answers
a) f(x) = 2(3) +1
f(x) = 7
bi) f(2)=2^2+4(2)-3
f(2)=4+8-3
f(2)=9
ii) f(0) = 0^2+4(0)-3
f(0)=0+0-3
f(0)=-3
iii) f(-3)=-3^2+4(-3)-3
f(-3)=9-12-3
f(-3)=-6
iv) f(x+1)=(x+1)^2+4(x+1)-3
f(x+1)=(x+1)(x+1)+4x+1-3
f(x+1)=x^2+2x+1+4x+4-3
f(x+1)=x^2+6x+2
Example 6
If f(x)=5-3x and g(x)=x^2+4, find (fog)(x)
Answer
(fog)(x)=5-3(x^2+4)
(fog)(x)=5-3x^2-12
(fog)(x)=-3x^2-7
Example 7
f(x)=5-3x and g(x)=x^2+4. Find (fog)(3) according IB Mathematics curriculum
Answer
g(3)=3^2+4
g(3)=13
(fog)(3)=5-3(13)
(fog)(3)=-34
Example 8
Given f(x)=2(x)+1 and g(x)=x^2-2, find
a) (fog)(x)
b) (fog)(4)
Answers
a) (fog)(x) = 2(x^2-2)+1
(fog)(x)=2x^2-3
b) (fog)(4)=2(4)^2-3
(fog)(4)=29
End of this part!
Drafted by Gina