Mathematics

Mathematics, 11.10.2019 03:00, TJxx187

Afunction f(x)=3x+12.
a determine the inverse of this function and name it g(x)
b. use composite functions to show that these functions are inverse
c. evaluate f(g(- explain? what is the domain?

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answer

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Answer

answered: nanagardiner08

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_______________

• Function: f(x) = 3x + 12.

A. Finding the inverse of f.

The composition of f with its inverse results in the identity function:

(f o g)(x) = x

f[ g(x) ] = x

3 · g(x) + 12 = x

3 · g(x) = x – 12

x – 12
g(x) = ⸺⸺
   3

   x
g(x) =  ⸺ – 4 <——— this is the inverse of f.
3

________

B. Verifying that the composition of f and g gives us the identity function:

• $\mathsf{(f\circ g)(x)}$

$\mathsf{=f\big[g(x)\big]}\\\\\\ \mathsf{=3\cdot \left(\dfrac{x}{3}-4\right)+12}\\\\\\
\mathsf{=\diagup\hspace{-7}3\cdot \dfrac{x}{\diagup\hspace{-7}3}-3\cdot 4+12}\\\\\\
\mathsf{=x-12+12}\\\\
\mathsf{=x\qquad\quad\checkmark}$

and also

• $\mathsf{(g\circ f)(x)}$

$\mathsf{=g\big[f(x)\big]}\\\\\\ \mathsf{=\dfrac{f(x)}{3}-4}\\\\\\ \mathsf{=\dfrac{3x+12}{3}-4}\\\\\\
\mathsf{=\dfrac{\diagup\hspace{-7}3\cdot (x+4)}{\diagup\hspace{-7}3}-4}\\\\\\
\mathsf{=x+4-4}\\\\
\mathsf{=x\qquad\quad\checkmark}$

________

C. Since f and g are inverse, then

f(g(– 2))

= (f o g)(– 2)

= – 2 ✔

• Call h the compositon of f and g. So,

h(x) = (f o g)(x)

h(x) = x

As you can see above, there is no restriction for h. Therefore, the domain of h is R (all real numbers).

I hope this helps. =)

Answer

answered: Guest

stop using this to cheat on home work

step-by-step explanation:

dfbvfvdf

Answer

answered: Guest

answer:

payment just for service

→

$

87.12

payment for service including tax

→

$

94.09

explanation:

service only with 20% tip

→

$

72.6

(

1

+

20

100

)

=

$

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the

service

−−−−−−

so technically the answer is

→

$

72.6

(

1

+

20

100

)

=

$

87.12

however, the intention of the question provider may have been that your answer is to be

$

87.12

(

1

+

8

100

)

=

$

94.09

to 2 decimal places.

'

payment just for service

→

$

87.12

payment for service including tax

→

$

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge

.

→

$

72.60

20% tip

20

100

×

$

72.60

=

$

14.52

−−−−−−

←

add

$

87.12

tax

8

100

×

$

87.12

=

$

6.97

−−−−−

←

add

$

94.09

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