Question

can someone please figure this out for me or at least explain this because im lost here

Let f(x)=3x+2, g(x)=x3−3x2+2x+11, and h(x)=x2−3. Perform the following operations.

a) g(-2)=
b) h(-1)=
c) g(x) - h(x)=__x^3 +__x^2+__x+__
d) -2f(x) * h(x)= __x^3+__x^2+__x+__
e) f(h(x)) = __x^2+__x+__
f) f(g(x)) =__x^3+__x^2+__x+__

Answer 1

Answer:

Step-by-step explanation:

the concepts are confusing of what a function is.   f(x)  seems mysterious , huh

it's just a way to give a label to some set of terms.  Just think of it as a name of a person, but in a generic sense, like   hey "guy"   or hey "gal"  you can address many people that way.  f(x) is doing that same thing addressing by a name,  a set of math terms.  

a)  

in a)  we are addressing the g(x) function and we are also sending that function the number -2 as an input. so find the g(x) function and put in (-2) everywhere that there is an "x" , so

g(x)=$x^{3}$-3$x^{2}$+2x + 11

g(-2) = $(-2)^{3}$-3$(-2)^{2}$+2(-2)+11

g(-2) = -8 -3(4) - 4 +11

g(-2) = -8 -12 -4 + 11

g(-2) = -24 + 11

g(-2) = -13

b)  

h(-1)  find the h(x) function and input a negative 1 where ever there is an x

h(x) =

h(-1) = $(-1)^{2}$ - 3

h(-1) = 1 - 3

h(-1) = -2

c)

for c)  just combine like terms of the two given functions

g(x) - h(x)  =  $x^{3}$-3$x^{2}$+2x + 11 - ($x^{2}$ - 3)

g(x) - h(x)  = $x^{3}$-3$x^{2}$+2x + 11 - $x^{2}$ + 3

g(x) - h(x)  = $x^{3}$-4$x^{2}$+2x + 14

d)

-2f(x) - h(x) = -2(3x + 2) - ($x^{2}$ - 3)

-2f(x) - h(x) = -6x - 4 - $x^{2}$ + 3

-2f(x) - h(x) = -6x - 1 - $x^{2}$

-2f(x) - h(x) = - $x^{2}$ - 6x - 1

e)

f(h(x))  this gets a bit more confusing b/c it's  a composition of functions,  that's just a fancy way of saying the functions are nested. one inside the other.

f(x) = 3x + 2

h(x) = $x^{2}$ - 3

plug h(x) in to f(x) where ever there is an x in f(x)   , luckily there is only one x in f(x)  :)

f(h(x)) = 3($x^{2}$ - 3) + 2

f(h(x)) = 3$x^{2}$ - 9 + 2

f(h(x)) = 3$x^{2}$ - 7

f(h(x)) = 3$x^{2}$ + 0x + (-7)  

f)

f(x) = 3x + 2

g(x) = $x^{3}$-3$x^{2}$+2x + 11

f(g(x)) = 3($x^{3}$-3$x^{2}$+2x + 11) + 2

f(g(x)) = 3$x^{3}$-9$x^{2}$+6x + 33 + 2

f(g(x)) = 3$x^{3}$-9$x^{2}$+6x + 35

Hope that helps :)