f(x)=(x+a)/b
or bf(x)=x+a
let f(x)=y
by=x+a
flip x and y
bx=y+a
or y=bx-a
or f^{-1}(x)=bx-a
also g(x) is inverse of f(x)
bx-a=cx-d
so b=c,a=d
again let g(x)=y
y=cx-d
flip x and y
x=cy-d
cy=x+d
y=(x+d)/c
or g^{-1}(x)=(x+d)/c
also f(x) is inverse of g(x)
so (x+a)/b=(x+d)/c
so a=d,b=c
so in either case a=d,b=c
take b=c=1
a=d=2
f(x)=(x+2)/1=x+2
g(x)=1x-2=x-2
so f(x) and g(x) are two parallel lines f(x) with y- intercept=1 and slope 0
g(x) with y-intercept -2 and slope 0
if we take b=c=2,a=d=3
f(x)=(x+3)/2=x/2+3/2
g(x)=2x-3
here f(x) is of slope 1/2 and y-intercept 3/2
g(x) is of slope 2 and y intercept -3
part 3.
f(f(x))=g((x+a)/b)=c[(x+a)/b]-d=(c/b)(x+a)-d
Answer:
-1.0 and 1
Step-by-step explanation:
Answer:
n = 13.
Step-by-step explanation:
Slope of the line = (10-1)/3-0) = 3
So the equation of the line is:
y - 1 = 3(x - 0)
y = 3x + 1
When x = 4 y = n, so:
n = 3(4) + 1 = 13.
n = 13.
Answer:
attached below
Step-by-step explanation:
a) Diagram of state transition representing failure and repair process of component
attached below
b) expression for the system to be completely available
attached below
c) Expression for system to be operating in a degraded mode
attached below
