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# Functions

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1. Hello everyone,

I'm having trouble with question 3c in the attachment - I have found when f(x) = x (x= -2 or 4/3 I think), but I don't get how to write the inequality bit? Do I write two inequalities or is only one of these values possible to use?
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2. Add y = x to your graph and compare with y = f(x).

If you know the intersections, the solution to the inequality is given where the function is lower than the y=x graph.
3. (Original post by Alexion)
Add y = x to your graph and compare with y = f(x).

If you know the intersections, the solution to the inequality is given where the function is lower than the y=x graph.
So... f(x) < -2 ?
4. (Original post by Electrogeek)
So... f(x) < -2 ?
and...
5. (Original post by Alexion)
and...
f(x) < 4/3?
6. (Original post by Electrogeek)
f(x) < 4/3?
You actually want it in terms of x, not f(x), my bad

so it's x < -2 and x > 4/3
7. (Original post by Alexion)
You actually want it in terms of x, not f(x), my bad

so it's x < -2 and x > 4/3
Thanks! I think I get it now - so it was asking which values of x would give a value which is less than the points of intersection?.

Also, if I'm told to deduce the number of roots of 2x+3=2x^2 (for example), is that the x-coordinates for the point(s) of intersection?
8. (Original post by Electrogeek)
Also, if I'm told to deduce the number of roots of 2x+3=2x^2 (for example), is that the x-coordinates for the point(s) of intersection?
The roots would be the points of intersection, yes.

However, if a question simply asked you to deduce the number of roots, it would be 2; if you turned it into one function (= 0) then it'd be a quadratic (i.e. two roots). The other way would be to quickly sketch both graphs which would indicate both intersections.
9. (Original post by Alexion)
The roots would be the points of intersection, yes.

However, if a question simply asked you to deduce the number of roots, it would be 2; if you turned it into one function (= 0) then it'd be a quadratic (i.e. two roots). The other way would be to quickly sketch both graphs which would indicate both intersections.
Cool - Thanks!

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