Simplifying help!!!?

Question

The original equation is f(x)=(2x+1)/(x+3)

I am fairly confident the inverse is F(x)=(-3x+1)/(x-2)

Now i must prove them alegebraically

I have tried many times and failed- help please!!!

Answer 1

Lets say y = f(x)

then original equation becomes

y=(2x+1)/(x+3)

=> xy + 3y = 2x + 1

=> xy - 2x = 1 - 3y

=> x (y-2) = (1-3y)

=> x = (1-3y)/(y-2)

So, the inverse function F(x)=> (1 -3x)/(x-2)

Answer 2

Hi,

....... .2x + 1

f(x) = ---------- is the same as

... ......x+ 3

.... .2x + 1

y = ----------

......x+ 3

The inverse of this function is formed by reversing the letters.

.... .2y + 1

x = ----------

......y+ 3

Multiply by y + 3 on both sides to eliminate the fraction.

x(y + 3) = 2y + 1

Distribute to eliminate parentheses. Move all terms with a "y" to one side and all terms without "y" to the other side.

xy + 3x = 2y + 1

xy - 2y = 1 - 3x

Factor out "y" as a GCF. Then divide to get y alone.

y(x - 2) = 1 - 3x

......1 - 3x

y = --------

.......x - 2

This is the inverse you got, so you are correct.

I hope that helps!! :-)

Answer 3

if F(X) is the inverse, then f(F(X)) = x, and F(f(x)) = x

try to calculate f(F(X)) and F(f(x)).

f(F(X)) = [2F(X)) - 1 ] / [F(X) +3] = [2 *(-3x+1)/(x-2) - 1 ] / [(-3x+1)/(x-2) +3]

do the same for F(f(x)).

good luck!

Answer 4

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