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: c=5.4
The two roots are 3/5 and 9/5
Step-by-step explanation:
assume 5x2−12x c=0 is supposed to be 5x^2 - 12x + c = 0
p = (12 + sqrt(144-20c))/10
q = (12 - sqrt(144-20c))/10
p-3q=0,
1.2 + 0.1sqrt(144-20c) +
-3.6 + 0.3sqrt(144-20c) = 0
-2.4 + 0.4sqrt(144-20c) +2.4 = 2.4
sqrt(144-20c) = 2.4/0.4 = 6
144-20c=36
144-36=20c
c = 108/20 = 5.4
5x^2-12x+5.4=0
x = 3/5 or x = 9/5
*triple phytagoras*
first triangle h = second triangle h = 24 in
x = 7 (triple phytagoras)
Answer: 12
Explain: Hope this helps!
1.1 Factoring: 4x2+9y2+16z2-6xy-12yz-8xz
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -6xy-12yz
Group 2: 16z2-8xz
Group 3: 4x2+9y2
Pull out from each group separately :
Group 1: (x+2z) • (-6y)
Group 2: (x-2z) • (-8z)
Group 3: (4x2+9y2) • (1)
Looking for common sub-expressions :
Group 1: (x+2z) • (-6y)
Group 3: (4x2+9y2) • (1)
Group 2: (x-2z) • (-8z)
