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xeze [42]
3 years ago
14

Let f(x) = -6x + 3 and g(x) = 5x + 4. Find fg and state its domain.

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
7 0

Answer:

f(g(x))=-30x-21

The domain is all real numbers

Step-by-step explanation:

we have

f(x)=-6x+3

g(x)=5x+4

we know that

(fog)(x)=f(g(x))

In the function f(x) substitute the variable x by the function g(x)

so

f(g(x))=-6(5x+4)+3

f(g(x))=-30x-24+3

f(g(x))=-30x-21

This is a linear function (equation of a line)

The domain is all real numbers

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Answer:

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Next the inner rectangle needs to be subtracted.  First though, we need its width, which we're not directly given.

We do however know the width of the entire shape, and the width of segments left after cutting out the inner rectangle.  All we need to do then is subtract the later from the former to the the inner rectangle's width:

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