Will tip fg for help with these;



1) Find the inverse function to f(x)=x^2 - 4, provided x≥4.





2) Let f(x) = 3x-5÷2 and g(x)=2x+5÷3, show that f(x) and g(x) are inverses to each other.






3) Let f(x) = 3x - 7 and g(x)=x^2-4x+9. Find (f o g)(-3):

Given a bijection f, the inverse function g is such that : g ( f(x) ) = f ( g(x) ) = x for every x in the correct domain.

1) the inverse g is such that :
f (g(x)) = x
g(x) ² - 4 = x
g(x) ² = x + 4
g(x) = √ ( x+4 )

2) Estimate f ( g(x) ) :
f ( g(x) ) = f ( (2x+5)/3 ) = [ 3 * (2x+5)/3 - 5 ] / 2 = [ 2x+5 - 5] / 2 = 2x / 2 = x

3) (f o g)(-3) = f ( g(-3) )
g(-3) = (-3)² - 4*(-3) + 9 = 9 + 12 + 9 = 30
f(30) = 3*30 - 7 = 90 - 7 = 83

On a sidenote, this is not "trigonometry"

This post was edited by feanur on Jul 5 2015 11:16am