Given f(x) and g(x) below, find:
(a) f+ g (b) f- g (c) f*g (d)f/g
Please show all of your work.
f(x) = �ãx
g(x) = 6x-5
To find the desired expressions, we need to perform the corresponding operations on the given functions. Let's start by finding:
(a) f + g
To find f + g, we add the two functions f(x) and g(x) together. We simply sum the corresponding terms. Therefore:
f(x) + g(x) = x + (6x-5) = x + 6x - 5 = 7x - 5
(b) f - g
To find f - g, we subtract the function g(x) from f(x). We subtract the corresponding terms. Therefore:
f(x) - g(x) = x - (6x-5) = x - 6x + 5 = -5x + 5
(c) f * g
To find f * g, we multiply the two functions f(x) and g(x) together. Multiply each term of f(x) by each term of g(x) to get:
f(x) * g(x) = x * (6x-5) = 6x^2 - 5x
(d) f / g
To find f / g, we divide the function f(x) by g(x). Divide each term of f(x) by each term of g(x) as follows:
f(x) / g(x) = x / (6x-5)
Now we have the four expressions:
(a) f + g = 7x - 5
(b) f - g = -5x + 5
(c) f * g = 6x^2 - 5x
(d) f / g = x / (6x-5)
So, this is the work involved in finding the expressions f+g, f-g, f*g, and f/g given f(x) = x and g(x) = 6x-5.