Determine the domain of the function (f o g)(x) where f(x)= 3/x+2 and g=5/x.

Mathematics

1 answer:

vitfil [10]3 years ago

7 0

Answer:

The Domain is all real values of x except x = 0 and x = -2.5.

Step-by-step explanation:

I am assuming that f(x) = 3/(x + 2).

(f o g)x is found by substituting 5/x for the x in 3/(x + 2).

(f o g) x = 3/ ( 5/x + 2)

= 3 / ( 5+2x) / x

= 3x / (5 + 2x).

When finding the domain you first check for values of x which make g(x) undefined then values of x which make (f o g)(x) undefined.

x = 0 makes g(x) = 5/0 so it is undefined and x = -2.5 makes g o f undefined also.

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Answer:

Part A: D. $y = (x + 1)(x+3)\\$

Part B: C. $3x(x-3) = 0\\$

Step-by-step explanation:

For part A) we just have to plug in 0 for x and solve for y until we find the equation that says 3 is the value for y when x is 0. For purposes of speeding up the process the correct answer is D. I will show how to check for it now.

The equation: $y = (x + 1)(x+3)$

Now plug in 0 for x.

$y = (0 + 1)(0+3)\\$

Now solve.

y = (1)(3)

y = 3

This proves that this is the correct answer.

For part B) we just have to plug in the give values for x separately and check for each value of x that it equals 0. For the purpose of speeding up the process the correct answer is C. I will show how to check for it now.

The equation: $3x(x-3) = 0$