Question

f(x)=(5X+1)/(4-3x)

1.what is its domain?
2.does it have an inverse? if it does, what is the domain of the inverse(that would be the range of f)

Answer 1

i think one of the domain is X not equal to 4/3

Answer 2

set the denominator = to zero
(4-3x)=0
4/3=x
so its range is all reals except were x = 4/3

Answer 3

\[x \in R, x \neq 4/3\]

Answer 4

does it have an inverse?

Answer 5

\[f^{-1}(x)=\frac{4x-1}{5+3x}\]

Answer 6

(1) the
domain is all reals except x=4/3
(2) \[y=\frac{5x+1}{4-3x}\]
\[(4-3x)y=4x+1\]
\[4y-3xy=4x+1\]
\[-3xy-4x=1-4y\]
\[x(-3y-4)=1-4y\]
\[x=\frac{1-4y}{-3y-4}\]
\[f^{-1}(x)=\frac{1-4x}{-3x-4}\]
domain of f inverse is all read numbers except when -3x-4=0 (x=-4/3)
so the range of f is all real numbers except x=-4/3

Answer 7

u did a mistake myininaya

Answer 8

(4-3x)y=5x+1 not 4x+1

Answer 9

probably my screen wouldn't stay still the latex was making it go crazy

Answer 10

i see it lol you are right i wrote down the correct thingy and then i wrote down the wrong thingy oh well at least it doesn't change the domain and range

Answer 11

yes but the inverse function is changed

Answer 12

oh wait it does change it
we hav3e -3x-5 in the bottom not -3x-4

Answer 13

-3x-5=0 when x=-5/3
so domain of f inverse is all real numbers but x=-5/3
so the range of f is all real numbers but x=-5/3

Answer 14

yes..now thats rigth myininaya . i have done it u can check..

Answer 15

no its cool
its late and i should go to bed

Answer 16

thank you everyone for your generous help