A function composition problem

[Raghav Gupta]

Homework Statement

If $f(x) = sin^2x + sin^2(x+ π/3) + cosxcos(x+ π/3)$ and $$g(5/4)=1$$, then $(gof)(x)$ is equal to?
Options are
0
1
sinx
None of these

Homework Equations

I know gof(x) is g(f(x)) but here g(x) is not given.

The Attempt at a Solution

Basically I think we have to put f(x) value in g(x) but here g(x) is not given,
What's the use of g(5/4) ?

 

[Mark44]

Homework Statement

If $f(x) = sin^2x + sin^2(x+ π/3) + cosxcos(x+ π/3)$ and $$g(5/4)=1$$, then $(gof)(x)$ is equal to?
Options are
0
1
sinx
None of these

Homework Equations

I know gof(x) is g(f(x)) but here g(x) is not given.

The Attempt at a Solution

Basically I think we have to put f(x) value in g(x) but here g(x) is not given,
What's the use of g(5/4) ?

Use trig sum formulas to simplify $f(x) = sin^2x + sin^2(x+ π/3) + cosxcos(x+ π/3)$. If you're careful, you can get this simplfied a great deal.

 

[Raghav Gupta]

Use trig sum formulas to simplify $f(x) = sin^2x + sin^2(x+ π/3) + cosxcos(x+ π/3)$. If you're careful, you can get this simplfied a great deal.

By simplifying I got,
$5/4 + \frac{√3}{2}sin2x$.

 

[Raghav Gupta]

Sorry, carefulness was required as you said.
Got on simplifying now 5/4, and then the answer is 1.
Thanks for the motivation of simplifying.

 

[Mark44]

Sorry, carefulness was required as you said.
Got on simplifying now 5/4, and then the answer is 1.
Thanks for the motivation of simplifying.

Yes, that's what I got as well.

 

[HallsofIvy]

Since the only g value you were given was "5/4", if this problem had an answer it had to be 5/4! Of course, you needed Mark44's suggestion to show that it had a solution.

 

[Raghav Gupta]

Ya sometimes applying common sense is of great use but I was thinking something else.