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garik1379 [7]
3 years ago
7

Determine the domain of the function (f*g)(x) where f(x) =3x-1/x-4 and g(x) =x+1/x

Mathematics
1 answer:
BARSIC [14]3 years ago
8 0

Answer:

Domain = R- {0,4}

Step-by-step explanation:

f(x) =\frac{3x-1}{x-4}

g(x) =\frac{x+1}{x}

(f*g)(x)=\frac{3x-1}{x-4} \times \frac{x+1}{x}

(f*g)(x)=\frac{(3x-1)(x+1)}{(x-4)(x)}

In order to function (f*g)x to be defined , the Denominator must not be equal to zero.

Hence

x ≠ 0

(x-4) ≠ 0 ⇒ x≠4

Hence (f*g)x is defined for all values of x except 0 and 4

Hence Domain = R- {0,4}

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Lee has $1.75 in dimes and nickels. The number of nickels is 11 more than the number of dimes. How many of each coin does he hav
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Answer:

Lee has 19 nickels and 8 dimes

Step-by-step explanation:

hello, I think I can help you with this

Step 1

Let

value of a nickel=$0.05

value of a dime=$0.10

number of nickels=N

number of nickels=D

According to the question data Lee has $1.75 in dimes and nickels.

0.05N+0.1D=1.75,equation(1)

also, the number of nickels is 11 more than the number of dimes.mathematical speaking

N=11+D,equation(2)

Step 2

replace N from equation (2) into equation (1)

0.05N+0.1D=1.75

0.05(11+D)+0.1D=1.75

Now, solve for D

0.55+0.05D+0.1D=1.75

0.15D=1.75-0.55

D=1.2/0.15

D=8

Step 3

replace the value of D into equation(2) to obtain N

N=11+8

N=11+8

N=19

Hence, Lee has 19 nickels and 8 dimes

Have a great day.

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