few functions questions

Jul 2010
8
0
So i just did a practice exam.. since i cant find any solutions anywhere i thought i would verify questions im not sure about.

1.) g(x) = x^2+3
h(x)= sqrt(x)

evaluate g(h(5))

h(5) = sqrt(5)
g(h(5))= (sqrt(5))^2+3
= 5+3 = 8

is that right?


2.) for inverse functions you just reverse the values so for
A(1,3) B(2,4)

inverse is
A(3,1) B(4,2)
?

3.) for function y=loge(x) apply following transformations

reflection in x axis
= -loge(x)
reflection in y axis
= -loge(-x)
dilation by factor 3 in x axis
= -3loge(-x)
dilation by factor 1/2 in y axis
= -3loge(-2x)
translation 4 right 1 up
-3loge(-2x-4)+1

is this right? im not sure