Question

Find (f∘g)(2) for the following functions.

f(x)=x^3+x^2 and g(x)=x^2−5

(f∘g)(2) =

Answer 1

@vocaloid

Answer 2

(f∘g)(2)

first calculate g(2) by plugging x = 2 into g(x) = x^2−5

take the end value from that, plug that into f(x)

Answer 3

g(2) = x^2 - 5

Answer 4

= -1

Answer 5

f(-1) = x^2-5 ?

Answer 6

check your math again

f(x)=x^3+x^2
f(-1) = (-1)^3 + (-1)^2 = -1 + 1 = 0

Answer 7

f(x)=|x| and g(x)=x^2/3

Find the formula for (f/g)(x) and simplify your answer.

(f/g)(x) =

Answer 8

you have to enter an absolute value sign for this one

f(x)=|x|
g(x) = x^2 - 3

so f/g is simply \[\frac{ |x| }{ x^{2}-3 }\]

Answer 9

that's not right

Answer 10

ah sorry g(x) is x^(2/3)

\[\frac{ |x| }{ x^{2/3} }\]

please check to make sure the denominator matches your g(x)

Answer 11

that's right

Answer 12

Consider the following functions.

f(x)=|x| and g(x)=x^2/3

Find the domain for (fg)(x). Express your answer in interval notation.

Answer 13

fg(x) is f multiplied with g

so fg is simply |x| * (x^2/3)

|x| has no restrictions on domain because you can enter any x-value into it

x^(2/3) is a bit different. we can re-write this as \[\sqrt[3]{x^{2}}\]

the inside of the square root must be at least 0, so x must be at least 0

Answer 14

i thought it was (-∞, ∞)

Answer 15

yeah nvm that's right, you can enter any value into x^(2/3) so there are no restrictions on domain

Answer 16

mines wasn't right

Answer 17

it says interval notation in domain

Answer 18

what did you enter? this? (-∞, ∞)

Answer 19

yes

Answer 20

can you take a screengrab of the problem

Answer 21

okay

Answer 22

ohh there was a division sign

because x^(2/3) is in the denominator, x^(2/3) cannot be 0, and thus x cannot be 0

so the domain is every value *except* 0

or (-∞, 0) ∪ (0, ∞)

Answer 23

the last one was right

Answer 24

Find (f∘g)(1) for the following functions. Round your answer to two decimal places, if necessary.

\[f(x) = \sqrt{x+3} \] and \[g(x) = 4 + \sqrt{x}\]

Answer 25

(f∘g)(1)

calculate g(1) by plugging in x = 1 into g(x)

then take the end result from that, plug it into f(x)

Answer 26

6

Answer 27

check your arithmetic again

g(1) = 4 + sqrt(1) = 5

f(5) = sqrt(5 + 3) = sqrt(8) = 2sqrt(2)

Answer 28

okay the answer is 8

Answer 29

no, not just 8, it's sqrt(8) or 2.82 rounded

Answer 30

they won't allow me sqrt8

Answer 31

you can convert it to a decimal, which would be 2.83

Answer 32

Given f(x), find g(x) and h(x) such that f(x)=g(h(x)) and neither g(x) nor h(x) is solely x.

\[f(x) = \sqrt{-x^2 + 3} - 4\]

Answer 33

g(x) =

h(x) =

Answer 34

think of the whole function as being made of two parts

sqrt(-x^2 + 3) and the -4 part

if we let h(x) = \[\sqrt{-x^{2}+3}\]then we can simply let g(x) = x - 4 to get f(x) = g(h(x)) = \[\sqrt{-x^{2}+3}-4\]

Answer 35

it's not working

Answer 36

did you enter h(x) = sqrt(-x^2 + 3) and g(x) = x - 4

Answer 37

yes but it said try again

Answer 38

is the function you typed exactly as it appears in the problem?

Answer 39

yes i'll send a pic

Answer 40

the order matters, you swapped h and g

Answer 41

oh i'm sorry

Answer 42

no wonder it was wrong

Answer 43

Consider the following functions.
\[f(x) = \sqrt{x+2} \] and \[g(x) = \frac{ x+2 }{ 3 }\]

Find the formula for (f∘g)(x) and simplify your answer. Then find the domain for (f∘g)(x). Round your answer to two decimal places, if necessary.

Answer 44

(f∘g)(x) =

Domain =

Answer 45

Domain : [-8, ∞)

Answer 46

if i'm right

Answer 47

domain looks good

what did you get as the function?

Answer 48

i didn't get one , i tried to solve it but it didn't look like it

Answer 49

remember, (f∘g)(x) means take g(x), plug it into f(x)

g(x) = (x+2) / 3

now take f(x) = sqrt(x+2), plug in x = (x+2) / 3, simplify

Answer 50

f(x) = sqrt(x+2) / 3 like this ?

Answer 51

\[f(x) = \sqrt{x+2} \] and \[g(x) = \frac{ x+2 }{ 3 }\]
plugging in g(x) into f(x) gives us

\[f(g(x))=\sqrt{\frac{ x+2 }{ 3 }+2}\]
simplify

Answer 52

f = sqrt3(x + 8)/3gx

Answer 53

your solution should not have the letter g in it anywhere, just x's. review operations with fractions when you get a chance.

\[f(g(x))=\sqrt{\frac{ x+2 }{ 3 }+2}\]

\[f(g(x))=\sqrt{\frac{ x+2 }{ 3 }+\frac{ 2*3 }{ 3 }}\]

\[f(g(x))=\sqrt{\frac{ x+2 }{ 3 }+\frac{ 6 }{ 3 }}\]
combining the fractions
\[f(g(x))=\sqrt{\frac{ x+2+6 }{ 3 }}\]
distributing
\[f(g(x))=\sqrt{\frac{ x+8 }{ 3 }}\]

Answer 54

oh okay , i see your point

Answer 55

Consider the following functions.

f(x)= √x+2 and g(x)=x+2/3

Find the formula for (g∘f)(x) and simplify your answer. Then find the domain for (g∘f)(x). Round your answer to two decimal places, if necessary.

Answer 56

(g∘f)(x) =

Domain =

Answer 57

similar logic, but make sure to pay attention to the order: because it's (g∘f)(x) (with g first) it means you take f(x) and plug it into g(x).

Answer 58

Domain : [-8, ∞)

Answer 59

(g∘f)(x) = f(g(x)) = x+5/3

Answer 60

your square root sign shouldn't have disappeared when you plugged f(x) into g(x)

Answer 61

also can you take a screengrab of this problem

Answer 62

ok, so let's start with g(x)

\[g(x)=\frac{ x+2 }{ 3 }\]
now, let's replace that x, by plugging in f(x) = sqrt(x+2) where the x is

\[g(f(x))=\frac{ \sqrt{x+2}+2 }{ 3 }\]

Answer 63

can you try finding the domain from that? remember that square root of something must be 0 or greater

Answer 64

[-2, ∞)

Answer 65

good