Question

which of the following statements have the same result? explain each step in solving each one. 1. f(3) when f(x)=2x+32. f^-1(3) when f(x)=2x-9/33. 5y+13=4y+4(10 points)

Answer 1

`\begin{gathered} I.f(x)=2x+3 \\ f(3)=2(3)+3=6+3=9 \end{gathered}`
`f(x)=(2x-9)/(3)`

Let's find the inverse function:

1. replace f(x) with y

`y=(2x-9)/(3)`

2. Replace every x with a y and every y with an x:

`x=(2y-9)/(3)`

3. solve for y:

`y=(3x+9)/(2)`

4. replace y with f^-1(x)

`f^(-1)(x)=(3x+9)/(2)`

Now:

`f^(-1)(3)=(3(3)+9)/(2)=(9+9)/(2)=(18)/(2)=9`

since the functions are equal for x = 3 we can conclude that they have the same result

`f(3)=f^(-1)(3)`