Question

Functions f and g are defined by f:x→ax-b,where a and b are constants and g:x→x+5.Given that fg(1)=11 and gf(2)=8.

Calculate the values of a and b?

What are the values of fg(-1)and gf(3)

Answer 1

fg(x) = ag-b = a(x+5)-b = ax+5a-b
fg(1) = 6a-b = 11

gf(x) = f+5 = ax-b+5
gf(2) = 2a-b+5 = 8 or 2a-b = 3
So,
4a = 8
a = 2
b = 1

fg(x) = 2x+9
gf(x) = 2x+4

and so on