Need help with functions!! (1 Viewer)

[adonis1]

ok im in year 11 so dont get technical with me:

Im currently using maths in focus an need help with Ex. 5.3 if you dont have this book ill type out the questions.

(oh and keep in mind '^' means to the power of e.g x^2= x squared)

Q2) If f(x)= x^3 + 1, find
(a) f(x^2)
(b) [f(x)]^2
(c)f(-x)
Is it an odd or even function

Q3) Show that g(x)=x^8+3x^4-2x^2 is an even function

Q4)Show that f(x) is odd, where f(x)= x

Q5) Show that f(x)=x^2-1 is an even function

Q6) Show that f(x)= 4x-x^3 is an odd function

Q7) Prove that f(x)= x^4+x^2 is an even function. Hence f(x)-f(-x)


Sorry that there are many questions, its just that im not good at them lol...id also appreciate it alot if you would show working.

Cheers

 

[adonis1]

thanks for replying everyone....*awkard silence, crickets churping, tumble weed*

 

[FinalFantasy]

Q2) If f(x)= x^3 + 1, find
(a) f(x^2)
(b) [f(x)]^2
(c)f(-x)
Is it an odd or even function

a) f(x^2)=(x²)^3+1=x^6+1 even
b)[f(x)]^2=(x³+1)²=x^6+2x³+1 neither even nor odd
c)f(-x)=-x³+1 neither even nor odd

Q3) Show that g(x)=x^8+3x^4-2x^2 is an even function
g(-x)=(-x)^8+3(-x)^4-2(-x)^2=x^8+3x^4-2x^2
g(x)=g(-x) .: even

Q4)Show that f(x) is odd, where f(x)= x
f(-x)=-x=-f(x) .: odd

Q5) Show that f(x)=x^2-1 is an even function
f(-x)=(-x)^2-1=x^2-1=f(x) .: even
Q6) Show that f(x)= 4x-x^3 is an odd function
f(-x)=-4x+x^3=-f(x) .: odd

Q7) Prove that f(x)= x^4+x^2 is an even function. Hence f(x)-f(-x)
f(-x)=(-x)^4+(-x)^2=x^4+x^2=f(x) .: even
f(x)-f(-x)=f(x)-f(x)=0

 

[adonis1]

thank you very-verry verrrrrrrrryyyyyyyyyy verryyyyyyyyy much. good luck with the hsc if ur in year 12

 

[FinalFantasy]

lol thx verrrrrrrry veerrrrrrrry verrrrrrrrrrrrryyyyyyyy much!