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Verifying an inverse of a function help?

Hello.

I have the function f(x)=2x^4 - 5

I have solved for y, and have found the inverse of this function as:-

g(x)= the 4th root of x+5 over 2. (Hard to type).

I have verified with g(f(x)), and as a result I got x. (So it looks like it's correct.)

However I am struggling to verify with f(g(x)), which should also turn out to be x, if I'm correct.

Could you please help with the last part.........

I've simplified it down to 2 x (square root of (x+5 over 2)) - 5

Thanks! :-)

Answers (3)

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aa10395375 profile image
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t5nrj6txaa profile image

y = 2x^4 - 5

y + 5 = 2x^4

((y+5)/2)^(1/4) = x Note that the 2 is INSIDE the radical, it is not (y+5)^(1/4)/2

using g(x) = ((x+5)/2)^(1/4) in f(x) you get

2((x+5)/2)^(1/4))^4 - 5 = 2(x +5)/2 - 5 = x + 5 - 5 = x

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0856772c9343 profile image

I dont think this function is invertible. It is not one to one. for example f(-1) = f(1) = -3. so if you want to inverse f at -3, it doesnt know whethere to go to -1 or 1.