# Thread: Operation on two functions

1. ## Operation on two functions

Hi everyone,

I know that it may sound like a dumb problem to solve for most of you, but I am a bit rusty and I'm doing my Calculus course remotely. In my first homework, there is a problem where I need to do this:

f(x)=(√(1-3x))/(x^3)
g(x)=x^2-x-1

(fg)(4)

When I look at this, It seems impossible to me, but Mathway seems to find that the answer is 4.
I get stuck at the point where everything is now equal to (√(-11))/(64))*(11)
To me it cannot be solved, am I wrong?

Thank you to anyone who took the time to read and consider my issue.

2. ## Re: Operation on two functions

Hey someone.

The notation (fg)(x) is such that you work out u = g(x) first and then f(u) after-wards.

Doing the calculation gives us:

g(4) = 4^2 - 4 - 1 = 11

f(11) = SQRT(1 - 3*11)/11^3 = -SQRT(32)/11^3

Note the definition of composition I'm using can be found here:

Function composition - Wikipedia, the free encyclopedia.

Doing it the other way gives us:

f(4) = SQRT(-11)/64

g(f(4)) = -11/64^2 + SQRT(-11)/64 - 1

You may want to bring this up with your tutor.

3. ## Re: Operation on two functions

Hi Chiro,

Thank you for showing me the alternate way you used. The maths you wrote in your post really helped me to understand function operations more easily.

I'll be sure to discuss that with my tutor once I have the opportunity to do so.