SOLUTION: 16 pts) Let f(x)=(3x -7)/(5x - 8) (a) Determine f -1 , the inverse function of f. Show work. (b) Determine the doma

Algebra ->  Equations -> SOLUTION: 16 pts) Let f(x)=(3x -7)/(5x - 8) (a) Determine f -1 , the inverse function of f. Show work. (b) Determine the doma      Log On


   

Question 1135756: 16 pts) Let f(x)=(3x -7)/(5x - 8)
(a) Determine f -1 , the inverse function of f. Show work.





















(b) Determine the domain of f. What is the domain of the inverse function?








(c) Determine f (3). f (3) = ______
work/explanation optional





(d) What is f -1 ( ____ ), where the number in the blank is your answer from part (c)?
work/explanation optional
 

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Let f%28x%29=%283x+-7%29%2F%285x+-+8%29++

(a) Determine f+%5E-1 , the inverse function of f. Show work.

f%28x%29=%283x+-7%29%2F%285x+-+8%29++ ....since f%28x%29=y+, we have

y=%283x+-7%29%2F%285x+-+8%29++ ................swap x and y

x=%283y+-7%29%2F%285y+-+8%29++ ................solve for y
x%285y+-+8%29+=3y+-7+
5xy+-+8x=3y+-7+
5xy+-+3y=8x+-7+
%285x+-+3%29y=8x+-7+
y=%288x+-7%29%2F%285x+-+3%29+
=>f+%5E-1=%288x+-7%29%2F%285x+-+3%29+


(b) Determine the domain of f. What is the domain of the inverse function?

f%28x%29=%283x+-7%29%2F%285x+-+8%29++
domain: exclude x value that makes denominator equal to zero
5x+-+8=0++->x+=8%2F5++

so, domain is: { x element R : x%3C%3E8%2F5 }


(c) Determine f+%283%29.
plug in x=3
f%283%29=%283%2A3+-7%29%2F%285%2A3+-+8%29++=%289-7%29%2F%2815-8%29=2%2F7

f+%283%29+=2%2F7


(d) What is f^ -1 ( ____ ), where the number in the blank is your answer from part (c)?
f+%5E-1=%288x+-7%29%2F%285x+-+3%29+...........if x=2%2F7
f+%5E-1=%288%282%2F7%29+-7%29%2F%285%282%2F7%29+-+3%29+
f+%5E-1=%2816%2F7+-49%2F7%29%2F%2810%2F7+-+21%2F7%29+
f+%5E-1=%28+-33%2Fcross%287%29%29%2F%28+-+11%2Fcross%287%29%29+
f+%5E-1=+-33%2F-+11%29+
f+%5E-1=+3+
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