a twist on Combining Functions

[shmurkles2]

Hey,

g(x)=(5x-3)/x+3

k(x)=(x)/x+3

What is m(x) if g(x)=k(m(x)) ?

I've never seen a problem like this in my life. Thanks for any help!

 

[Steven G]

Is g(x) = (5x-3)/x + 3 or is it (5x-3)/(x+3)? I'll assume the 2nd one.

k(anything) = anything/(anything + 3)

So k(m(x)) = m(x)/( m(x) + 3) and you want this to equal g(x) which is (5x-3)/(x+3).

Now continue from here.

 

[shmurkles2]

Is g(x) = (5x-3)/x + 3 or is it (5x-3)/(x+3)? I'll assume the 2nd one.

k(anything) = anything/(anything + 3)

So k(m(x)) = m(x)/( m(x) + 3) and you want this to equal g(x) which is (5x-3)/(x+3).

Now continue from here.

you literally just restated the question...

 

[pisrationalhahaha]

you literally just restated the question...

Just cross multiply and take m(x) as a common factor

 

[Dr.Peterson]

you literally just restated the question...

Restating a problem in a clearer form is often the first, and most important, step in solving it!

You now have m(x)/(m(x) + 3) = (5x - 3)/(x + 3). So solve the equation m/(m + 3) = (5x - 3)/(x + 3) for m.

 

[Steven G]

you literally just restated the question...

I do not think that I just restated the problem.

 

[shmurkles2]

Restating a problem in a clearer form is often the first, and most important, step in solving it!

You now have m(x)/(m(x) + 3) = (5x - 3)/(x + 3). So solve the equation m/(m + 3) = (5x - 3)/(x + 3) for m.

Perfection at last. Thanks!