# math

posted by .

The function f(x)=2x+8/3x-7 is one to one. Find its inverse, and check your answer.
f^-1(x)=

I haven't one clue how to do this...help me pleaaaase someone!

• math -

let y = (2x+8)/(3x-7) , notice the brackets are essential

step1: interchange the x and y variables to form the initial inverse.

x = (2y+8)/(3y-7)

step: solve this new equation for y

3xy - 7x = 2y+8
3xy - 2y = 7x + 8
y(3x - 2) = (7x + 8)
y = (7x + 8)/(3x - 2)

f^-1 (x) = (7x + 8)/(3x - 2)

test with some value of x, say x = 3
f(3) = 14/2 = 7
f^-1 (7) = should get 3 back ..
= (49+8)/(21-2) = 57/19 = 3 , looks ok

## Similar Questions

1. ### Pre-Calc

Does y=1/x have an inverse? It is a one-to-one function, so it should be the inverse equation is the same?
2. ### Algebra-One to one function

Could you please check my answers and help me with one of them?
3. ### Algebra Help Inverse One-to-one

Did I do this right? Problem: If the following defines a one-to-one function, find its inverse. If no, write "Not one-to-one." {(-2,4),(-1,4),(0,1),(1,-5)} answer: Not one-to-one because of (-2,4), (-1,4)

The following function is one-to-one; find its inverse f(x)=x^3+5 I know that the first step would be to set y = to x so I did y=x^3+5 Then you swap x with y so x=y^3+5. Then you solve for y and this is where I think i messed up. I …
5. ### college alg

the function f(x)=6x+9/3x-7 is one to one. find its inverse and check your answer. f^-1(x)=?
6. ### algebra

1. the function f(x)=6x/3x-5 is one to one. find its inverse and check your answer. And on the second one can you tell me if I am correct. 2. solve the following exponential solution 7^2x+7^x+1-60=0 7^2 x+7^x-59=0 (49x)+7^x-59=0 49x/49=0/49 …
7. ### College math

Determine whether the following function is a one-to-one function,and if the function is a one-to-one, find a formula for the inverse. F(x)=5/(x+3)
8. ### College math

Determine whether the following function is a one-to-one function,and if the function is a one-to-one, find a formula for the inverse. F(x)=(5x-6)/(2x+3)
9. ### College math

Determine whether the following function is a one-to-one function,and if the function is a one-to-one, find a formula for the inverse. F(x)=x^3-27
10. ### Math

Find inverse of f if f(x)= x^2-4x+3, (for x is smaller than and equal to 2). First prove that f(x) is one to one in the defined domain of f and then obtain the inverse function. I know how to find the inverse. We just switch x and …

More Similar Questions