Question

Please help me answer these.

Answer 1

Hello!

The best way to solve this is to replace X for Y, and Y for X.

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A sample problem to help:

4x +8 = y  

4y +8 = x  (switched X and Y)

Y + 8 = 1/4x (solve for Y)

-8            -8

y = 1/4x -8

(now your almost done, since this is function, we need to change y to be f(x))

f(x) = 1/4 - 8

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Now that you have a basic understanding, let's do the ones you listed!

We are looking to see if the equations are inverses of the equation.

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1. f(x) = 2/3x - 7         g(x) = 3/2x + 7

First: You use equation f(x), and change f(x) to y:

y = 2/3x - 7

Next: You switch x and y:

x = 2/3y - 7

Now solve for y.

x = 2/3y - 7

+7            +7

x + 7 = 2/3y

$*\frac{3}{2}$       $*\frac{3}{2}$

y = $\frac{3}{2}x$ + 5

(Set it to f(x) )

f(x) = $\frac{3}{2}x$ + 5

Now look to see if it matches with the second equation.

f(x) = $\frac{3}{2}x$ + 5     g(x) = 3/2x + 7

It doesn't, so it is not the inverse of each other.

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2. f(x) = -2x - 1           f(x) =-1/2x - 1/2

First: You use equation f(x), and change f(x) to y:

y = -2x - 1

Next: You switch x and y:

x = -2y - 1

Now solve for y.

x = -2y - 1

+1        +1

x + 1 = -2y

/-2   /-2

-1/2x + 1/2 = y

(Set it to f(x) )

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

Now look to see if it matches with the second equation.

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

It does, so it is the inverse of each other.

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3. f(x) = $\frac{x+1}{2}$               g(x) = 2x - 1

First: You use equation f(x), and change f(x) to y:

y = $\frac{x+1}{2}$

Next: You switch x and y:

x = $\frac{y+1}{2}$

Now solve for y.

x = $\frac{y+1}{2}$

*2    *2

2x = y + 1

-1        -1

y = 2x - 1

(Set it to f(x) )

f(x) = 2x - 1

Now look to see if it matches with the second equation.

f(x) = 2x - 1     g(x) = 2x - 1

It does, so it is the inverse of each other.

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I hope this helps,

-Oceanbreeze24