SOLUTION: 15) f (x) = 5x-1/2x+3 find the inverse function f^-1 (x) a) -1-3x/2x-5 b) -1-3x/2x+5 c) 2x+5/1+3x d) 5x-1/2x+3 e) 1-5x/3+2x

Algebra ->  Trigonometry-basics -> SOLUTION: 15) f (x) = 5x-1/2x+3 find the inverse function f^-1 (x) a) -1-3x/2x-5 b) -1-3x/2x+5 c) 2x+5/1+3x d) 5x-1/2x+3 e) 1-5x/3+2x       Log On


   

Question 122528: 15) f (x) = 5x-1/2x+3 find the inverse function f^-1 (x)

a) -1-3x/2x-5
b) -1-3x/2x+5
c) 2x+5/1+3x
d) 5x-1/2x+3
e) 1-5x/3+2x

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 15

f%28x%29=%285x-1%29%2F%282x%2B3%29 Start with the given function


x=%285f%28x%29-1%29%2F%282f%28x%29%2B3%29 Switch the x and f(x) variables. Now the goal is to solve for f(x)


x%282f%28x%29%2B3%29=5f%28x%29-1 Multiply both sides by 2f%28x%29%2B3


2x%2Af%28x%29%2B3x=5f%28x%29-1 Distribute


2x%2Af%28x%29%2B3x-5f%28x%29=-1 Subtract 5f(x) from both sides


2x%2Af%28x%29-5f%28x%29=-1-3x Subtract 3x from both sides


f%28x%29%282x-5%29=-1-3x Factor out f(x) from the left side


f%28x%29=%28-1-3x%29%2F%282x-5%29 Divide both sides by 2x-5 to isolate f(x)



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Answer:

So the inverse function is

f%5E%28-1%29%28x%29=%28-1-3x%29%2F%282x-5%29


So the answer is A)