Application of Functions

Question

Determine f^-1(x) if f(x) = x+2 / x-3, where x not equal 3

Answer 1

First thing you need to do is substitute f^-1(x) with y. Now, you substitute x with y, and y with x. Finally, we solve for y.

f^-1(x) = (x+2)/(x+3)

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

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

Multiply the fraction by y+3 to get rid of the denominator. What you do on one side, you do it on the other.

x(y+3)=y+2

Distribute the x on the left.

xy+3x=y+2

Subtract the 2 to get y by itself.

xy+3x-2=y

Move over the -3x+2 using inverse operations to the right and y to the left, using inverse operations.

xy-y=-3x+2

Factor out the y on the left

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

Divide the x+1 on both sides to get y by itself.

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

Finally replace y with f^-1(x) and that is your final answer.

f^-1(x)= (-3x+2)/(x+1)



Hope you find this helpful.

Answer 2

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