What is the range of f(x)=x^4-4x^2 ?

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

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range of f(x)=x^4-4x^2

range

f (x) = 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

2 cos (6 x + \frac{π}{2})

f (x) = \frac{5 - 2 x}{6 x + 3}

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

f (x) = - 4 - \frac{9}{2} x

2^{x} - 5