quadratics question please help!!

The function f is such that f(x)=2x-3 for x=>k, where k is a constant.
The function g is such that g(x)=x^2-4 for x=> -4.
Find the smallest value of k for which the composite function gf can be formed

Reply 1

old_engineer

What have you tried? Where are you stuck?

Reply 2

Forregi88

Original post by old_engineer

What have you tried? Where are you stuck?

ive found gf and found the two x, i dont know how to find k

Reply 3

old_engineer

Original post by Alevels0521

ive found gf and found the two x, i dont know how to find k

The thing to do is to write gf as g(f(x)) which in turn becomes (f(x))^2 -4. Now have a look at the domain limit for g and see how that relates to f(x).

Reply 4

Forregi88

Original post by old_engineer

The thing to do is to write gf as g(f(x)) which in turn becomes (f(x))^2 -4. Now have a look at the domain limit for g and see how that relates to f(x).

yeah, i got the point. the answer is supposed to be -1/2 but my answer is 3/2. how do you get -1/2??

Reply 5

old_engineer

Original post by Alevels0521

yeah, i got the point. the answer is supposed to be -1/2 but my answer is 3/2. how do you get -1/2??

Best if you post your working.

Reply 6

Forregi88

Original post by old_engineer

Best if you post your working.

This is my working

F585DDF8-BD39-4926-A427-F7203F54F8E4.jpeg203.6KB

Reply 7

old_engineer

Original post by Alevels0521

This is my working

The domain restriction for g(x) is x >= -4
From that, it follows that the domain restriction for g(f(x)) is f(x) >=4. This is just by putting f(x) in place of x.

Reply 8

mistermew72

2x - 3 = -4 not 0
2x = -1
x= -1/2

(edited 5 years ago)

Reply 9

Forregi88

Original post by old_engineer

The domain restriction for g(x) is x >= -4
From that, it follows that the domain restriction for g(f(x)) is f(x) >=4. This is just by putting f(x) in place of x.