How do you find the inverse function of #f(x) = (2x-3)/(x+4)#?

Answer 1

Cora Alexander

You can swap #x# with #y# and solve for #y#.

#y = f(x) = (2x - 3)/(x+4)#

#x = (2y - 3)/(y+4)#

#xy + 4x = 2y - 3#

#4x + 3 = 2y - xy#

#4x + 3 = (2 - x)y#

#y_"inv" = f_("inv")(x) = (4x + 3)/(2-x)#

#f(x) = (2x - 3)/(x+4)#: graph{y = (2x - 3)/(x+4) [-20, 20, -10, 10]}

#f_("inv")(x) = (4x + 3)/(2-x)#: graph{y = (4x + 3)/(2-x) [-20, 20, -10, 10]}

http://www.wolframalpha.com/input/?i=inverse+of+y+%3D+%282x-3%29%2F%28x%2B4%29

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email

Answer 2

Elijah Allen

To find the inverse function of $f(x) = \frac{2x-3}{x+4}$ :

Replace $f(x)$ with $y$ .
Swap $x$ and $y$ to obtain $x = \frac{2y - 3}{y + 4}$ .
Solve this equation for $y$ .
First, multiply both sides by $y + 4$ to eliminate the denominator.
Then, distribute to get $x(y + 4) = 2y - 3$ .
Expand: $xy + 4x = 2y - 3$ .
Rearrange terms: $xy - 2y = -4x - 3$ .
Factor out $y$ : $y(x - 2) = -4x - 3$ .
Divide both sides by $x - 2$ : $y = \frac{-4x - 3}{x - 2}$ .
Replace $y$ with $f^{-1}(x)$ to get the inverse function.

Therefore, the inverse function is $f^{-1}(x) = \frac{-4x - 3}{x - 2}$ .

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.