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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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Since segment AC bisects (aka cuts in half) angle A, this means the two angles CAB and CAD are the same measure. I'll refer to this later as "fact 1".

Triangles ABC and ADC have the shared segment AC between them. By the reflexive property AC = AC. Any segment is equal in length to itself. I'll call this "fact 2" later on.

Similar to fact 1, we have angle ACB = angle ACD. This is because AC bisects angle BCD into two smaller equal halves. I'll call this fact 3

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To summarize so far, we have these three facts

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Once we prove the triangles are congruent, we use CPCTC (corresponding parts of congruent triangles are congruent) to conclude that AB = AD and BC = BD. These pair of sides correspond, so they must be congruent in order for the entire triangles to be congruent overall.

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