abbie1
Help!! Let f(x)=7x-13. Find f^-1(x).
Let f(x)=x^2-16. Find f^-1(x).
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saifoo.khan
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Do you know how to find an inverse?
abbie1
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Okay thanks..
hartnn
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ask if you still need help.
abbie1
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I'm still confused..what am I finding the inverse to in my problem?? @hartnn
hartnn
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ok, let y=7x-13
now to find the inverse, isolate x =... ?
then just replace 'x' and 'y' (you can replace before isolating also.)
abbie1
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-7x=-13-y?? why would there be a y in there??
abbie1
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and then divide the whole thing by -7, but they're going to be fractions.
hartnn
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y= 7x-13
add 13 to both sides,
then divide by 7 [Let there be fractions, its ok]
abbie1
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So basically you set the problem equal to 7x-13, and either make it equal to y or x?? There is no y in the problem? that's why i am confused
abbie1
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x=-13-y/-7, and then do you want me to solve for x on y=7x-13 or that's what y equals?? So you use x to solve for y and y to solve for x??
ohimai
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y = f(x).. They are the same thing
abbie1
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x and y are the same thing??????
hartnn
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i considered f(x) = y for simplicity.
i'll write out steps so that you can understand.
y= 7x-13
y+13 = 7x
x = (y+13)/7
now to find inverse function just replace x and y
y= (x+13)/7
so your inverse function is
\[f^{-1}(x)=\dfrac{x+13}{7}\]
got this ?
ohimai
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f(x) and y are the same thing, so you re-write it as y = 7x-13
ohimai
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got that part?
abbie1
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Yes THANK YOU!!!!
ohimai
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swop d x for d y.... it becomes x = 7y-13
hartnn
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can you do same thing for
f(x)=x^2-16. ?
ohimai
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yep
ohimai
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after swopping, solve for y
ohimai
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7y= x+13
y = (x+13)/7
abbie1
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Yes x=4 + sqrt y
ohimai
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yes, but u have to swop d x and d y back... final answer would be y = 4 + sqrt(x)
hartnn
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did u simplify like this ? \[\sqrt{16+y}=4+\sqrt y \]
no, thats incorrect.
abbie1
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by d do you mean the?
ohimai
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yep
abbie1
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sqrt. y+16=x^2 (Root over y+16)
hartnn
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yeah,
the inverse function will be \[f^{-1}(x)=\sqrt{x+16}\]
no further simplification possible.
hartnn
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ok ? got it ?
abbie1
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Oh got it!!!