Question

The functions f and g are defined by

f:x ---> 3x+2 x all Real numbers
g:x ---> {6 over 2x+3} " xnotequalto -1.5

Answer 1

find the value of x for which fg(x) = 3

Answer 2

does x=3?

Answer 3

f(g(x)) = 3(6/(2x+3)) +2
= 18/(2x+3) + 2
therefore 18/(2x+3) + 2 = 3
so 18/ (2x+3) = 1.
so 2x+3 = 18
so 2x = 15
so x = 7.5

Answer 4

OK

Answer 5

(ii) says sketch, in a single diagram, the graphs of y=f(x) and y=f^-1(x), making clear the relationship between the two graphs

Answer 6

is f^-1 y=x-2 over 3?