Question

Use the following functions, to find the three answers.

f(x) = x + 5
g(x) = x2 -4x + 5
h(x) = 3x2 - 2x + 5


Find (f+g)(x)
Find (f*h)(x)
Find f [g(2)]

Answer 1

just plug in :)

Answer 2

yeah
(f + g)(x) => f(x) + g(x)

Answer 3

Distribute (f+g)(x)=f(x)+g(x)

Answer 4

(f*h)(x)
f(x)*h(x) you dont really distribute but that is what it really means. Shorthand i think.

Answer 5

Oh...I get it now thank you, my math book doesn't really explain it at all.

Answer 6

so the first one. If
f(x)=x + 5
and
g(x) = x2 -4x + 5

then f(x) + g(x) ... plug in

^ ^
(x + 5 ) + (x2 -4x + 5)


now simply add like terms. SInce it is addition you can get rid of the perenthesis.

Answer 7

Thank you that explains it really good

Answer 8

Find (f*h)(x) that one is almost the same

f(x)*h(x)

so multiply
f(x) = x + 5
h(x) = 3x2 - 2x + 5


plug in

(x + 5)*(3x2 - 2x + 5)

here the perenthesis do matter so distribute the x+5 :) Let me know if you need help with that

Answer 9

THis one is a lil more complex but still easy

Find f [g(2)] you got g(2) inside of f(x) right?

g(x)= x2 -4x + 5

However you probably know when you are given a number you evaluate

g(2)= (2)^2 -4(2) + 5=
4-8+5=
-4+5=1 so g(2)=1

that means

f [g(2)] and if g(2)=1 then f(1) now you simply plug in

f(x) = x + 5 is f(1) = (1) + 5 =6 so


f [g(2)]=6 if i didn't make any careless mistakes. THaat is called a composite function you will also see it written as

(f o g) (2) = f [g(2)] the o is the composite operator i think and i think that is the correct notation i dont really like it but i think that is the right alternative notation you will see.


Remember always do the inner most part first :D

Answer 10

Thanks this helps me a lot thanks