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AlekseyPX
3 years ago
11

F(x) = 4x + 4 g(x) = 3x +7

Mathematics
1 answer:
salantis [7]3 years ago
7 0

Answer:

Part 1) (f+g)(x)=7x+11

Part 2) (f-g)(x)=x-3

Part 3) (f/g)(x)=\frac{(4x+4)}{(3x+7)}

Part 4) In interval notation the domain is  (-∞,-7/3) ∪ (-7/3,∞)

Part 5) (f o g) (x)=12x+32

Step-by-step explanation:

we have

f(x)=4x+4

g(x)=3x+7

Part 1) Find (f+g)(x)

we know that

(f+g)(x)=f(x)+g(x)

substitute the given functions

(f+g)(x)=(4x+4)+(3x+7)

Combine like terms

(f+g)(x)=7x+11

Part 2) Find (f-g)(x)

we know that

(f-g)(x)=f(x)-g(x)

substitute the given functions

(f-g)(x)=(4x+4)-(3x+7)

(f-g)(x)=4x+4-3x-7

Combine like terms

(f-g)(x)=x-3

Part 3) Find (f/g)(x)

we know that

(f/g)(x)=\frac{f(x)}{g(x)}

substitute the given functions

(f/g)(x)=\frac{(4x+4)}{(3x+7)}

Part 4) What the domain for the answer in question 3

we have

(f/g)(x)=\frac{(4x+4)}{(3x+7)}

we know that

The denominator of the quotient cannot be equal to zero

so

3x+7=0

3x=-7

x=-\frac{7}{3}

The domain is all real numbers except the number x=-7/3

In interval notation the domain is  (-∞,-7/3) ∪ (-7/3,∞)

Part 5) Find (f o g) (x)

we know that

(f o g) (x)=f(g(x))

substitute

f(g(x))=4(3x+7)+4

f(g(x))=12x+28+4

f(g(x))=12x+32

therefore

(f o g) (x)=12x+32

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