Question 484794
If f(x)=-3x+2,what are the values of m and b so that f(mx+b)=2x-3?
<pre>
 
f(<font color="green">x</font>) = -3<font color="green">x</font> + 2

Repace <font color="green">x</font> by <font color="red">mx+b</font>

f(<font color="red">mx+b</font>) = -3(<font color="red">mx+b</font>) + 2

f(mx+b) = -3mx - 3b + 2

We are told that

f(mx+b) = 2x - 3

So

-3mx - 3b + 2 = 2x - 3  for all values of x

Therefore we set the coefficients of x equal:

          -3m = 2
            m = {{{-2/3}}}

And we set the constants equal:

      -3b + 2 = -3

          -3b = -5

            b = {{{(-5)/(-3)}}}

            b = {{{5/3}}}        


Edwin</pre>