SOLUTION: {{{ Let f (x) = 1/x^2 (sqrt(25 + x^2)) }}} {{{ and g(t) = 5 tan(t) for 0 < t < pi/2 }}} Find (f � g)(t) and simplify so that there are no radicals in the function. Write your an

Question 923726:
Find (f � g)(t) and simplify so that there are no radicals in the function. Write your answer in terms of sin(t) and cos(t).
(f � g)(t) =
There shouldn't be a parentheses around 25+x^2 just couldn't make it without one it seems
------------------------------------------------------------------

Find (f compose g)(t) and simplify. Write your answer in terms of sin t and cos t.
(f � g)(t) =
Please explain these
Thanks!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first one to get you started

(f � g)(t) is the same as . They are just two ways of saying the same exact thing.

Start with f(x)

Replace every x with g(t)

On the right side, replace all copies of g(t) with 5tan(t)

Square to get

Factor

Break up the root

Take the square root of 25

Use the trig identity

Take the square root of . Since , this means is positive.

Rewrite tan & sec in terms of sine & cosine.

Multiply and rearrange terms.

Flip the fraction (1/[a/b] = b/a)

Side Note: this only works when (in quadrant I and IV)

------------------------------------------------------------------------

Let me know if that helps or not. Thanks.

If you need more help, feel free to email me at jim_thompson5910@hotmail.com

My Website: http://www.freewebs.com/jimthompson5910/home.html

RELATED QUESTIONS
Let f (x) = (1/(x^2 sqrt(49 + x^2)) and g(t) = 7 tan (t) for 0 < t < pi/2 Find (f (answered by stanbon)

Let f (x) = 1 x2 100 + x2 and g(t) = 10 tan t for 0 < t < π 2 Find... (answered by Alan3354)

Composite trig function problem? Let f(x) = 4x/(√(1-x^2)) and g(t) = sin(t) for... (answered by stanbon)

Please help, so confused on how to solve this. Let {{{ g(t) = (2/7) csc(t) }}} for... (answered by stanbon)

Composite trig function problem? Let f(x) = 4x/(√(1-x^2)) and g(t) = sin t for 0 < (answered by jim_thompson5910)

{{{ Let f (x) = 6x/(sqrt(1 + x^2)) }}} and {{{ g(t) = tan(t) for 0 < t < pi/2 (answered by lwsshak3)

Let f (x) = 8x/(sqrt(1 - x^2)) and g(t) = sin(t) for 0 < t < pi/2 Find... (answered by stanbon)

Let {{{ g(x) = (x) sqrt(64x^2+25) }}} and {{{ h(t)=(5/8)cot(t) }}} for {{{ 0 (answered by Edwin McCravy)
Let g(x) = x√(64x^2+25) and h(t)=5/8 cot(t) for 0 (answered by stanbon)