Am I doing this correctly...
Here are a few more problems... The last one I am stuck on how to simplify it correctly.
1) f(x) = ((2x-3)/(-7x+5)) +5 g(x) = (3x-7)/(6x+5)
Find f of g:
Put the g(x) in:
(2((3x-7)/(6x+5))-3) / (-7((3x-7)/(6x+5))+5) +5
((6x-14)/(6x+5)) -3 / (((-21x+49)/(6x+5)) +5) +5
Multiply the -3 and f by (6x+5)/(6x+5) and then add or subtract
((24x-29)/(6x+5) / (9x+74)/(6x+5)) +5
I'm not sure if I dealt with the "+5" at the end of f(x) correctly...
2) Inverse of f(x) = ((2x-3)/(-7x+5)) +3
Multiply the 3 by (-7x+5)/(-7x+5)
y= ((2x-3)/(-7x+5)) + ((-21x+5)/(-7x+5))
That comes out to be:
y = (19x+12)/(-7x+5)
Switch the x's and y's:
x = (19y+12)/(-7y+5)
Multiply both sides by (-7y+5):
-7xy+5x = 19y+12
Switch the 5x with the 19y:
-7xy-19y = 12-5x
Factor out a y:
y(-7x-19) = 12-5x
y = (12-5x)/(-7x-19)
For this one, I'm not sure what I'm doing is called (sorry). My prof. has been doing them on the board and said to try a few different combinations at home. You should be able to pick up on what I'm doing, or trying to do anyway.
3) tan(cos^-1x + cot^-1y)
cosx= x/1 = adj/hyp
Missing triangle side is sqrt(1-x^2)
cotx= x/1 = adj/opp
Missing side is sqrt((x^2) + 1)
tan(alpha + beta) = (tan alpha + tan beta)/(1- (tan alpha)(tan beta))
Sub in from the triangles:
(((sqrt(1-x^2))/(x)) +((1)/(x))) / (1- ((sqrt(1- x^2))/(x))((1)/(x))
How do I simplify that correctly?
Would it be:
(sqrt(1-x^2) +1) / (1 - (sqrt(1-x^2))