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: