Inequality signs

[__SB]

Given that gf(x) < 5 for all values of x, find the set ofpossible values of b. Can anybody see where my slip with the sign is? Thanks

F(x) = 4x^2 -12x and g(x) = -x + b
Fg(x) = -(4x^2 – 12x) + b < 5
-4x^2 + 12x + b -5 < 0
4x^2 – 12x – b + 5 > 0
Using b^2 – 4ac
(-12)^2 – (4 * 4 * (-b + 5)) > 0 (mark scheme has this < 0 here )
144 + 16b – 80 > 0
64 + 16b > 0
16b > -64
B > -4 Answer is B<-4

 

[stapel]

Given that gf(x) < 5 for all values of x, find the set ofpossible values of b. Can anybody see where my slip with the sign is? Thanks

F(x) = 4x^2 -12x and g(x) = -x + b
Fg(x) = -(4x^2 – 12x) + b < 5
-4x^2 + 12x + b -5 < 0
4x^2 – 12x – b + 5 > 0
Using b^2 – 4ac
(-12)^2 – (4 * 4 * (-b + 5)) > 0 (mark scheme has this < 0 here )
144 + 16b – 80 > 0
64 + 16b > 0
16b > -64
B > -4 Answer is B<-4

How does "F" relate to "f"? Does "gf" mean "the functional value of g multiplied by the functional value of f", or does it mean "g composed with f"? If the latter (as it seems from your working above), on what basis have you decided that "Fg" is equivalent to "gf"? How does "b" relate to "B"? Also, how is this "Arithmetic", rather than algebra?

Thank you!

 

[pka]

Given that gf(x) < 5 for all values of x, find the set ofpossible values of b. Can anybody see where my slip with the sign is? Thanks
F(x) = 4x^2 -12x and g(x) = -x + b
Fg(x) = -(4x^2 – 12x) + b < 5
-4x^2 + 12x + b -5 < 0
4x^2 – 12x – b + 5 > 0

PLEASE do answer the question above.

Note that neither $\displaystyle F\circ g(x)\text{ NOR }F\cdot g(x)$.

 

[__SB]

PLEASE do answer the question above.

Note that neither $\displaystyle F\circ g(x)\text{ NOR }F\cdot g(x)$.

whats wrong with the above question? and im not really sure what you mean

 

[__SB]

How does "F" relate to "f"? Does "gf" mean "the functional value of g multiplied by the functional value of f", or does it mean "g composed with f"? If the latter (as it seems from your working above), on what basis have you decided that "Fg" is equivalent to "gf"? How does "b" relate to "B"? Also, how is this "Arithmetic", rather than algebra?

Thank you!

Where have I said fg(x) = gf(x) ?
and my bad B = b etc, didn't watch caps on word

 

[__SB]

Realised my error.
4x^2 – 12x – b +5 > 0
Therefore there is no solutions as the graph is above thex-axis.
Hence the discriminant has to be < 0

Thanks all for responses.