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Find the following

f(x)= 2x^2 + x -1 ; g(x)= 4x

a)
(f + g) (x) =

b)
(f-g)(x) =

c)
(f•g)(x) =

d)
(f/g) (x)

1 Answer

5 votes

Answer:

a) To find (f + g)(x), we need to add the two functions f(x) and g(x) together.

First, let's rewrite the functions in their expanded form:

f(x) = 2x^2 + x - 1

g(x) = 4x

Now, we can add the functions:

(f + g)(x) = (2x^2 + x - 1) + (4x)

Simplifying the expression by combining like terms, we get:

(f + g)(x) = 2x^2 + 5x - 1

So, (f + g)(x) is equal to 2x^2 + 5x - 1.

b) To find (f - g)(x), we need to subtract the function g(x) from f(x).

Rewriting the functions in their expanded form:

f(x) = 2x^2 + x - 1

g(x) = 4x

Now, we can subtract the functions:

(f - g)(x) = (2x^2 + x - 1) - (4x)

Simplifying the expression by combining like terms, we get:

(f - g)(x) = 2x^2 - 3x - 1

So, (f - g)(x) is equal to 2x^2 - 3x - 1.

c) To find (f • g)(x), we need to multiply the two functions f(x) and g(x) together.

Rewriting the functions in their expanded form:

f(x) = 2x^2 + x - 1

g(x) = 4x

Now, we can multiply the functions:

(f • g)(x) = (2x^2 + x - 1) * (4x)

To simplify this expression, we can distribute 4x to each term in the first function:

(f • g)(x) = 8x^3 + 4x^2 - 4x

So, (f • g)(x) is equal to 8x^3 + 4x^2 - 4x.

d) To find (f / g)(x), we need to divide the function f(x) by g(x).

Rewriting the functions in their expanded form:

f(x) = 2x^2 + x - 1

g(x) = 4x

Now, we can divide the functions:

(f / g)(x) = (2x^2 + x - 1) / (4x)

To simplify this expression, we divide each term in the numerator by the denominator:

(f / g)(x) = (2x^2 / 4x) + (x / 4x) - (1 / 4x)

Simplifying further, we get:

(f / g)(x) = 1/2 + 1/4 - 1/4x

So, (f / g)(x) is equal to 1/2 + 1/4 - 1/4x.a) To find (f + g)(x), we need to add the two functions f(x) and g(x) together.

First, let's rewrite the functions in their expanded form:

f(x) = 2x^2 + x - 1

g(x) = 4x

Now, we can add the functions:

(f + g)(x) = (2x^2 + x - 1) + (4x)

Simplifying the expression by combining like terms, we get:

(f + g)(x) = 2x^2 + 5x - 1

So, (f + g)(x) is equal to 2x^2 + 5x - 1.

b) To find (f - g)(x), we need to subtract the function g(x) from f(x).

Rewriting the functions in their expanded form:

f(x) = 2x^2 + x - 1

g(x) = 4x

Now, we can subtract the functions:

(f - g)(x) = (2x^2 + x - 1) - (4x)

Simplifying the expression by combining like terms, we get:

(f - g)(x) = 2x^2 - 3x - 1

So, (f - g)(x) is equal to 2x^2 - 3x - 1.

c) To find (f • g)(x), we need to multiply the two functions f(x) and g(x) together.

Rewriting the functions in their expanded form:

f(x) = 2x^2 + x - 1

g(x) = 4x

Now, we can multiply the functions:

(f • g)(x) = (2x^2 + x - 1) * (4x)

To simplify this expression, we can distribute 4x to each term in the first function:

(f • g)(x) = 8x^3 + 4x^2 - 4x

So, (f • g)(x) is equal to 8x^3 + 4x^2 - 4x.

d) To find (f / g)(x), we need to divide the function f(x) by g(x).

Rewriting the functions in their expanded form:

f(x) = 2x^2 + x - 1

g(x) = 4x

Now, we can divide the functions:

(f / g)(x) = (2x^2 + x - 1) / (4x)

To simplify this expression, we divide each term in the numerator by the denominator:

(f / g)(x) = (2x^2 / 4x) + (x / 4x) - (1 / 4x)

Simplifying further, we get:

(f / g)(x) = 1/2 + 1/4 - 1/4x

So, (f / g)(x) is equal to 1/2 + 1/4 - 1/4x.h

Explanation:

User Davideas
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