Let f(x)=3x^2+1 and g(x)=×+4

Question

Find (f-g)(x) state domain and range

(f+g)(x) state domain and range

Evaluate (f+g)(-5)

Evaluate (f-g)(-5)

Evaluate f(g(-5))

Evaluate g(f(2))

Answer 1

(f+g)(x) = f(x) + g(x). Similarly, (f-g)(x) = f(x) - g(x).

The domain is the set of all values that would work for x, i.e. produce a valid result. For instance, if h(x) = 1/x, the domain would be all real numbers except 0, because 1/0 is undefined.

The range is the set of all possible solutions. If h(x) = |x| then the range would be all positive real numbers.

To get (f+g)(-5) you can add the two equations first then plug in -5 for x to get a result. Similarly done for (f-g)(x).

To find f(g(x)), you can either first find g(x) then put that solution into f(x) or first find f(g(x)) by putting in (x+4) as "x" into f(x). i.e. f(g(x)) = f(x+4) = 3(x+4)²+1 then solve for f(g(-5)). Similarly done for g(f(x)).