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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)

Respuesta :

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

Let's find the inverse function:

1. replace f(x) with y

[tex]y=\frac{2x-9}{3}[/tex]

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

[tex]x=\frac{2y-9}{3}[/tex]

3. solve for y:

[tex]y=\frac{3x+9}{2}[/tex]

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

[tex]f^{-1}(x)=\frac{3x+9}{2}[/tex]

Now:

[tex]f^{-1}(3)=\frac{3(3)+9}{2}=\frac{9+9}{2}=\frac{18}{2}=9[/tex]

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

[tex]f(3)=f^{-1}(3)[/tex]

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