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maxonik [38]
3 years ago
11

Let f(x)=3x-6 and g(x)=x-2 find f(g(5))-ie. (f • g)(5) and its domain

Mathematics
1 answer:
Molodets [167]3 years ago
3 0

Solution for f(g(5)):


The notation f(g(5)) or (f • g)(5) means that we first plug 5 into the function g(x), simplify, then plug the answer that we got to f(x). We will do this step-by-step:


Step 1: Plugging 5 to g(x)

g(5)=5-2=3


Step 2: Plugging the answer to f(x)

f(3)=3(3)-6=9-6=3


ANSWER: f(g(5)) is equal to 3.


Domain:


For the function f(g(x)), we can find the domain by analyzing the domains of each individual functions separately and excluding certain values depending on the restrictions from the outermost function.


However, since both functions have all real numbers as its domain, we will not need to do any exclusion anymore.


ANSWER: The domain of the function is all real numbers.

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3 0
2 years ago
PLEASE HELP ASAP 25 PTS
olya-2409 [2.1K]

Hello from MrBillDoesMath!

Answer:

Choice B     (  (x+6)/5) )



Discussion:

y =  f(x) =  5x - 6

To solve for the inverse of f, replace "y" by "x" and "x" by "y" in the original equation. That is, solve for "y" in

x = 5y -6    =>                  add 6 to both sides

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y =  (x+6)/5

"y" above is the inverse, which is Choice B



Thank you,

MrB

4 0
3 years ago
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