<p>Take a step back and look at it this way: there is this function called g. It has a rule that is in the form g(x)= … some formula.</p>
<p>Now we are going to tell you that two different inputs to the function both have the same output. Then you will have to use that information to solve for some variable. And finallyyou will have to use that variable to evaluate the function at some new input.</p>
<p>The two inputs that give the same output are “k” and “2k+3”.<br>
So you are going to have to set up the equation g(k) = g(2k+3)</p>
<p>But then you have to “get rid of” the g’s by applying the rule for that particular function. What rule was that? Oh, yeah, it was g(x) = 2x +3. [It was obnoxious of them to use the same expression in two places…they did it to make this more confusing – and it seems to have worked 
] So anyway, you have to apply THAT rule to BOTH inputs.</p>
<p>The left side becomes 2k+3 and the right side becomes 2(2k+3) +3</p>
<p>The rest is just as teteatete said…</p>
<p>^ Except that I should have said -3 instead of +3 … d’oh</p>
<p>@cecillia</p>
<p>g(x)=2x-3
Therefore, g(k)=2k-3 (substituted k for x)</p>
<p>g(2k-3)= 2(2k-3)-3 = 4k-6-3= 4k-9</p>
<p>We want to find k, so we set g(k)=g(2k-3) and by substituting the above in, we get 2k-3=4k-9 </p>
<p>then go from there</p>
<p>hope that helps!</p>
<p>thanks cortana! so your saying that because both equations are for a single variable, we can interchange k and x? i just need verification! :)</p>
<p>“Why can we interchange k and x?” </p>
<p>Most function questions begin by defining the function. They say things like:</p>
<p>Let the function f be defined by f(x) = 10x +4</p>
<p>or </p>
<p>Let g be defined by g(x)=2x-3.</p>
<p>The words "…be defined by… are important. They tell you that the equation that follows is not just true for one particular value of the function – it’s the defining equation that is true for all of them.</p>
<p>At that stage, it didn’t matter what letter they used for the input. Defining a function with the equation f(x) = 10x + 4 is no different than defining it with f(t) = 10t + 4. You are still being told that the function takes inputs, multiplies them by 10 and then adds 4 to get the outputs. </p>
<p>Now, once the function has been defined, you can apply it to any input you like.</p>
<p>So AFTER you have been told that g is defined by g(x) = 2x - 3, you can then conclude that…</p>
<p>g(6) = 2 times 6 - 3</p>
<p>g(1000) = 2 times 1000 - 3</p>
<p>g(anything you like) = 2 times that thing - 3</p>
<p>and in this problem:</p>
<p>g(k) = 2k -3</p>
<p>g(2k-3) = 2 times (2k-3) -3 = 2(2k-3) -3 = 4k-9</p>
<p>and take it from there…</p>
<p>Sorry for the long answer.</p>