function f and g are defined as
f(x): x2-2x
g(x):2x+3 both x E R
1) find the set of values of x for which f(x)>15
2)find the range of f...
im bad at this...had nly 2 or 3 classes of it...n didnt get much
its ok with practice u will get better
1) f(x)>15
x
2-2x>15
x
2-2x-15>0
x
2-5x+3x-15>0
x(x-5)+3(x-5)>0
(x-5)(x+3)>0
(x-5))(x-(-3))>0
now theres a rule u need to keep in mind (i cant illustrate it here using a diagram so u will have to memorise it for the time being)
whenever an expression of the form(x-a)(x-b)>0 occurs where a<b then the solution is x<a and x>b
over here a is 5 and b is -3(5 is greater than -3)
so the solution is x<-3 and x>5
2)x
2-2x
=(x
2-2x+1)-1
=(x-1)
2-1
now u can see that when x=1
f(1)=(1-1)
2-1=-1
see for yourself that whatever value u put for x, the answer will always be greater than -1(-1 is the minimum value of f(x))
so the range of f(x) is f(x)>=-1