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Katieann16
 3 years ago
What is the inverse of the function f(x)=1/3x2?
Katieann16
 3 years ago
What is the inverse of the function f(x)=1/3x2?

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MathDad72
 3 years ago
Best ResponseYou've already chosen the best response.1y=(1/3)x2 Switch y&x and solve x=(1/3)y2

MathDad72
 3 years ago
Best ResponseYou've already chosen the best response.1So what is the next step you would do?

MathDad72
 3 years ago
Best ResponseYou've already chosen the best response.1So we want to get y by itself. Lets add 2 to each side.

MathDad72
 3 years ago
Best ResponseYou've already chosen the best response.1\[x+2 = \frac{ 1 }{ 3 }y\]

MathDad72
 3 years ago
Best ResponseYou've already chosen the best response.1Does that make sense?

MathDad72
 3 years ago
Best ResponseYou've already chosen the best response.1So how will we now "move" the 1/3?

Fall1213
 3 years ago
Best ResponseYou've already chosen the best response.0Okay. f(x)=1/3x2 Take f(x) = y y = 1/(3x  2) y*(3x  2) = 1 3xy  2y = 1 1  2y=  3xy (1 + 2y) = 3xy 1 + 2y = 3xy (1 + 2y)/y = 3x (1 + 2y)/3y = x Lastly, replace y with x, we have: (1 + 2x)/3x = y Which is the inverse.

Fall1213
 3 years ago
Best ResponseYou've already chosen the best response.0Wait, is it \[F(x) = \frac{ 1 }{ 3x  2 }?\]

Fall1213
 3 years ago
Best ResponseYou've already chosen the best response.0Or is it \[F(x) = \frac{ 1 }{ 3 }x  2?\]

MathDad72
 3 years ago
Best ResponseYou've already chosen the best response.1Wouldn't it be 3(x+2)=y y=3x+6 \[f ^{1}(x) = 3x+6\]

Katieann16
 3 years ago
Best ResponseYou've already chosen the best response.0thats what i got but i got 3x but i see what i did wrong, thank you
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