math cie question a level

HUSSAI55

can someone please do question 10 of p12 march feb 2018
ttps://paper.sc/search/?as=page&query=9709%20m18

Reply 1

Granadalad

Do you mean the functions question on page 16? If so which bit is presenting difficulty?

Reply 2

HUSSAI55

yes i dont get the first three parts :frown:

Reply 3

Granadalad

Original post by HUSSAI55

yes i dont get the first three parts :frown:

Range is the set of possible answers that the equation can produce. In part a) x can be fractionally bigger than 2 with no limit on how big it can become.

Now just consider this;
A fraction with a very very large denominator has a value of "next to nothing", ie approx zero. So 1/10000000000 is next to nothing.
A fraction with a denominator very close to zero has a very very large value, approaching infinity, eg 1/0.00000000000000000001

Substitute these 'limits in your equation to see how the answers (range) can vary.

In part b) substitute a value 'just' bigger than 2 and then just smaller than 4

Part c) referring to fg means f( fgx) ) or f( 8/(x-2) ) which means write f(x) replacing occurences of x with 8/(x-2)).
giving 8/( [8/(x-2)] - 2 ). Now consider what the result could be using the earlier constraints stated for x.

For clarity, if f(x) = x^2 and g(x) = x+2
f(3) = 3^2
g(5) = 5 + 2
and fg(x) = f(g(x)) = f( x+2) = (x+2)^2