I have a question, if f(x)=x/2 and g(x)=3x+1 find:

a) (f+g)(x) i know you go x/2+3x+1.
but how do i solve that??

b) (f-g)(x) i know you go x/2-3x+1,
how do i solve?

c)(f*g)(x) how do i solve?

(f/g)(x) how do i solve??

f(g(x)) how do i solve??
thanks for your itmeee

for (f+g)(x) you would add up your two function expressions and simplify them

so (f+g)(x) = x/2 + 3x+1
= x/2 + (6x+2)/2 = (7x+2)/2
which is not what you have

suppose we use x=4
f(4)= 4/2 =2
g(4) = 13
so (f+g)(4) = 15
in my (f+g)(x) = (7x+2)/2
(f+g)(4) = (7(4)+2)/2 = 15

for (f-g)(x) you would subtract the two functions,
for (f*g)(x) you would multiply them, etc

test your answers in a similar way to the one I showed you

thanks so much:)

To solve each of these equations, we simply substitute the given functions into the operations indicated. Let's go through each step-by-step:

a) To find (f + g)(x), we need to add the functions f(x) and g(x) together. So, substitute the functions into the equation: (f + g)(x) = f(x) + g(x) = (x/2) + (3x + 1).
To solve this, we just need to combine like terms. Distribute 1 to (x/2) to get: (f + g)(x) = x/2 + 3x + 1.

b) To find (f - g)(x), we need to subtract g(x) from f(x). Substitute the functions into the equation: (f - g)(x) = f(x) - g(x) = (x/2) - (3x + 1).
Again, to solve this, we combine like terms. Distribute -1 to (3x + 1) to get: (f - g)(x) = x/2 - 3x - 1.

c) To find (f * g)(x), we need to multiply f(x) by g(x). Substitute the functions into the equation: (f * g)(x) = f(x) * g(x) = (x/2) * (3x + 1).
To solve this, we multiply the terms together. Using the distributive property, we get: (f * g)(x) = (3x^2/2) + (x/2).

d) To find (f / g)(x), we need to divide f(x) by g(x). Substitute the functions into the equation: (f / g)(x) = f(x) / g(x) = (x/2) / (3x + 1).
To solve this, we divide the terms. We can simplify the expression by multiplying the numerator and denominator by 2, to eliminate the fraction in the numerator: (f / g)(x) = x / (2 * (3x + 1)).

e) To find f(g(x)), we need to substitute g(x) into f(x). Substitute the functions into the equation: f(g(x)) = f(3x + 1) = (3x + 1)/2.
No additional steps are needed here; we just replace x in f(x) with (3x + 1) to get the final result.

I hope this helps! Let me know if you have any further questions.