Question

How do you find `f(x)+g(x), f(x)-g(x), f(x)*g(x), (f/g)(x)` given `f(x)=3/(x-7)` and `g(x)=x^2+5x`?

Answer 1

For `f(x) + g(x)` , you just simply add the two functions. That is:

`f(x) + g(x) = 3/(x-7) + x^2 + 5x`.

For `f(x) - g(x)`, the same applies, but now we are subtracting the two functions; that is:

`f(x) - g(x) = 3/(x-7) - x^2 - 5x`.

And we proceed like this to the other two cases:

`f(x).g(x) = (3/(x-7)) . (x^2 + 5x) = (3(x^2 + 5x))/(x-7)`.

`f(x)/g(x)= (3/(x-7))/(x^2 + 5x) = (3)/((x-7)(x^2 + 5x))`.