Find (f + g)(x), (f - g)(x),...; (f o g)(x), (g o f)(x),....

[angel21]

1. For f(x) = x/x + 1 and g(x) = x^3, find:

(a). (f + g)(x)
(b). (f - g)(x)
(c). (fg)(x)
(d). (f/g)(x)

2.For f(x)= 3^sqrt (x – 1) and g(x) = x^3 + 1, find:

(a) f o g
(b) g o f
(c) f o f

 

[Deleted member 4993]

Re: Find (f + g)(x)?

1. For f(x) = x/x + 1 and g(x) = x^3, find:

(a). (f + g)(x)
(b). (f - g)(x)
(c). (fg)(x)
(d). (f/g)(x)

2.For f(x)= 3^sqrt (x – 1) and g(x) = x^3 + 1, find:

(a) f o g
(b) g o f
(c) f o f

These are fairly straight-forward problem - have you looked at the worked out examples of your textbook?

Please show us your work/thoughts - indicating exactly where you are stuck.

 

[stapel]

1) The operations work exactly as one would expect. For instance, (f - g)(x) = f(x) - g(x), and so forth.

2) If it helps, restate the compositions in the other form they taught you. For instance, (g o f)(x) = g(f(x)), and so forth.

:wink:

Eliz.

 

[nycfunction]

1. For f(x) = x/x + 1 and g(x) = x^3, find:

(a). (f + g)(x)
(b). (f - g)(x)
(c). (fg)(x)
(d). (f/g)(x)

I will do (a) and b for question 1. You can follow my steps to do the rest on your own.

For (a) we have (f + g)(x) = f(x) + g(x) You know the values of f(x) and g(x) as given to you: x/(x+1) plus x^3 We now add them together like we did with fractions. We have:

x/(x+1) PLUS x^3/1

Our LCD is (x+1) After doing the algebra, we get this:

(f + g)(x) = (x^4 + x^3 + x)/(x+1)....The numerator can be factored to give us:

(f + g)(x) = x(x^3 + x^2 + x)/(x + 1)...Final answer.

====================================

For (b) we have: (f - g)(x) = f(x) MINUS g(x) Again, plug and chug but this time we subtract.

x/(x+1) - (x^3/1)

After doing the algebra, we get:

(f - g)(x) = x(-x^3 - x^2 + 1)/(x + 1)

Notice that the quantity (x + 1) in the denominator continues to be our LCD.

Now, you try the rest.