Functions

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?

IMG_1245.jpg521.1KB

Reply 1

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.

Reply 2

Electrogeek

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 ?

Reply 3

Alexion

Original post by Electrogeek

So... f(x) < -2 ?

and...

Reply 4

Electrogeek

Original post by Alexion

and...

f(x) < 4/3?

(edited 7 years ago)

Reply 5

Alexion

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

Reply 6

Electrogeek

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?

(edited 7 years ago)

Reply 7

Alexion

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.