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maths functions q c3

can someone pls explain how part d of this question is done!!! why is it wrong to remove the modulus and solve for k and x by equating the twi equations?? what does the q even want :/ ..... like the way i thought of it was that k is a vertical transformatipon therefore it shifts the graph down then the graph will have two intersections with the x-axis and those are the two values
(edited 6 years ago)
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Original post by pondsteps
can someone pls explain how part d of this question is done!!! why is it wrong to remove the modulus and solve for k and x by equating the twi equations?? what does the q even want :/


f(x)=kf(x)=k means you looking for the points where the function y=f(x)y=f(x) and y=ky=k instersect. Obviously y=ky=k is a straight, horizontal line. So if you were to imagine that line on top of f(x)f(x), in what region would the line cut f(x)f(x) twice??
f(x)=k is just a horizontal line on the graph on the left. For it to have two solutions, what can you say about where the first (smaller x) one is?
(edited 6 years ago)
ok i just edited what i posted... why is the way that i thpught of the q wrong.. it makes sense being a vertical transformation..
Original post by RDKGames
f(x)=kf(x)=k means you looking for the points where the function y=f(x)y=f(x) and y=ky=k instersect. Obviously y=ky=k is a straight, horizontal line. So if you were to imagine that line on top of f(x)f(x), in what region would the line cut f(x)f(x) twice??


omg i gettttttttttttttt it!!!! thanks! how are we supposed to think of that in the middle of an exam????????????????????????????????????
Original post by pondsteps
ok i just edited what i posted... why is the way that i thpught of the q wrong.. it makes sense being a vertical transformation..


Er, sure you have do that but that would be the long way around it as that would require you to think more about it. Also by removing the modulus sign, you lose the V shape, so obviously it would be hard to tell at what points y=ky=k intersects f(x)f(x) twice... basically a lot more to consider. Much easier to do it from the graph.

Original post by pondsteps
omg i gettttttttttttttt it!!!! thanks! how are we supposed to think of that in the middle of an exam????????????????????????????????????


Dunno, just know that equations like these represent intersections between functions geometrically, I guess.

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