Let f (x)= x+1 and g (x)=1/x. Find (g/f)(x).

[bdemalin]

Good evening! I am attempting to solve this problem and for the most part I can start it off, however I'm not sure how to finish or solve it. This is what I have so far.

((1/x)/(x+1))(x)

I have tried to replace x with 1 to try to help me but I get 1/2 which is wrong.

Please help!

 

[Harry_the_cat]

Good evening! I am attempting to solve this problem and for the most part I can start it off, however I'm not sure how to finish or solve it. This is what I have so far.

((1/x)/(x+1))(x)

I have tried to replace x with 1 to try to help me but I get 1/2 which is wrong.

Please help!

Is (g/f)(x) the same as g(x)/f(x)?

 

[bdemalin]

Reply

I am not entirely sure. In my past experiences with this type of problem, the format has always been g of f, vice versa, or a simpler version of this troubling format. My brain tells me to begin solving the problem this way but then again the answers I come up with are incorrect.

 

[Otis]

((1/x)/(x+1))(x)

That's g divided by f (but not yet simplified), although we don't write function definitions like that. Function notation shows the name of the output variable to the left of an equals sign, and the definition goes to the right. Like this,

(g/f)(x) = (1/x)/(x+1)

Now, simplify the right-hand side.

I have tried to replace x with 1 to try to help me but I get 1/2 which is wrong.

g(1) = 1 and f(1) = 2, so g/f is 1/2.

Did somebody tell you that (g/f)(1) does not equal 1/2?

Cheers

 

[Otis]

Is (g/f)(x) the same as g(x)/f(x)?

Yup. Also,

(f+g)(x) = f(x) + g(x)

(g-f)(x) = g(x) - f(x)

(f*g)(x) = f(x)*g(f)