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## let f(x)=3x-6 and g(x)=x-2. find the g/f and state its domain.

SOLUTION: let f(x)=3x-6 and g(x)=x-2. find the g/f and state its domain.

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-> SOLUTION: let f(x)=3x-6 and g(x)=x-2. find the g/f and state its domain.

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Question 252676: let f(x)=3x-6 and g(x)=x-2. find the g/f and state its domain.

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Found 2 solutions by drk, Edwin McCravy:Answer by drk(1908) (Show Source):

You can put this solution on YOUR website! WE have two functions:(i) f(x)=3x-6(ii)g(x)=x-2Now, F(x) / g(x) will be(iii) 3x-6 / (x-2)At this point we must look at domain. We have variables in the denominator. Set the denominator = 0 and solve for x.x-2 = 0 – – > x = 2 is the restriction on the domain.Back to the fraction . . .We can factor the numerator as 3(x-2). We get(iv) 3(x-2) / (x-2) = 3.

Answer by Edwin McCravy(18579) (Show Source):

You can put this solution on YOUR website! Note: The other tutor mistakenly did f/g, not g/f.Solution by Edwin:,

This function g/f is not defined when the denominator

equals 0. The denominator would equal 0 when

which simplifies to when . Therefore

x cannot equal 2, and 2 cannot be part of the domain

of g/f. However when , the right side

can be simplified to

However that cancellation cannot be made when !,

since the function is undefined there, but it can be done

for every other value of x.

So therefore we can express g/f in its simplest form

this way:

,

Its graph is the green graph below. It is the horizontal

green line with a hole in it where the point (2,)

is missing and that point is NOT part of the graph of g/f:

So the domain of g/f is the x-axis without a value at 2.

In set-builder notation the domain of g/f would be

written .

The graph of its domain on a number line would look just

like the x-axis above only, shaded everywhere except at 2,

and with an open circle at 2, like this:

-4 -3 -2 -1 0 1 2 3 4

In interval notation this domain is written

Edwin

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Operations on Functions | Purplemath – Алгебра. Найти f(g(x)) f(x)=2x+5 , g(x)=3x-6.Question: Let F(x) = 3x – 6 And G(x)=x – 2. Find F/g And Its Domain. This problem has been solved! See the answer. Transcribed Image Text from this Question. Let f(x) = 3x – 6 and g(x)=x – 2. Find f/g and its domain.We have variables in the denominator. Set the denominator = 0 and solve for x. x-2 = 0 – – > x = 2 is the restriction on the domain. We can factor the numerator as 3(x-2).