What is the range of y=x^4-4x^2 ?

The range of y=x^4-4x^2 is f(x)>=-4

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range of y=x^4-4x^2

range

y = x^{4} - 4 x^{2}

f (x) \geq - 4

Interval Notation

[- 4, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

x^{4} - 4 x^{2}

Inverse of

x^{4} - 4 x^{2} : 2 + x + 4, - 2 + x + 4, 2 - x + 4, - 2 - x + 4

2 + x + 4, - 2 + x + 4, 2 - x + 4, - 2 - x + 4

Find the domain of each inverse function

Domain of

2 + x + 4 : x \geq - 4

Domain of

- 2 + x + 4 : x \geq - 4

Domain of

2 - x + 4 : - 4 \leq x \leq 0

Domain of

- 2 - x + 4 : - 4 \leq x \leq 0

Combine the intervals

f (x) \geq - 4

f (x) = - 2 (\frac{1}{4})^{x - 3}

f (x) = \frac{y ^{2} - 1}{y}

f (x) = (x - 3)^{2}

f (x) = \frac{4 - e ^{x^{2}}}{1 - e ^{4 - x^{2}}}

ln (x^{2} - 6 x + 8)