(Solved) What are the inverse functions of f(x)=3x^4 and f(x)=2-2x^2?

rjr862

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11 years ago

What are the inverse functions of f(x)=3x^4 and f(x)=2-2x^2?

This is for my Algebra II class.
I need to know the inverse functions of:
f(x)=3x^4
and
f(x)=2-2x^2
When you find the inverse function, there can not be a square root in the denominator if there is a fraction present in the answer. So you must get rid of the square root in the denominator. Thank you very much if you try and solve this question.

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fjohn14

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11 years ago

To find the inverse functions, change f(x) to y and then swap the x and y's, then solve for y

f(x) = 3x^4

y = 3x^4 (change f(x) to y)

x = 3y^4 (switch x and y)

x/3 = y^4 (divide by 3)

y = +/- (x/3)^(1/4)

The inverse functions are

y = (x/3)^(1/4)
y = -(x/3)^(1/4)
___________________________

f(x) = 2 - 2x^2

y = 2 - 2x^2

x = 2 - 2y^2

x - 2 = -2y^2 (subtract 2)

(x - 2)/-2 = y^2 (divide by -2)

(2 - x)/2 = y^2 (simplify the left side)

y = +/- sqrt[(2 - x)/2]

The inverse functions are

y = sqrt[(2 - x)/2]
y = -sqrt[(2 - x)/2]

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11 years ago

In all honesty neither have inverses as they are not 1 to 1 functions...now if you want to restrict the domains of each then these "new different" functions might have inverses.....f1(x) = 3 x^4 , x >/= 0 has y = fourth root of [ x/3], x >/= 0 as the inverse for f1(x)....domains are important when considering inverse functions

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fjohn14

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11 years ago

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What are the inverse functions of f(x)=3x^4 and f(x)=2-2x^2?

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