What is the range of f(x)=x^4-25x^2 ?

The range of f(x)=x^4-25x^2 is f(x)>=-625/4

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range of f(x)=x^4-25x^2

range

f (x) = x^{4} - 25 x^{2}

f (x) \geq - \frac{625}{4}

Interval Notation

[- \frac{625}{4}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

x^{4} - 25 x^{2}

Inverse of

x^{4} - 25 x^{2} : \frac{25 + 625 + 4 x}{2}, - \frac{25 + 625 + 4 x}{2}, \frac{25 - 625 + 4 x}{2}, - \frac{25 - 625 + 4 x}{2}

\frac{25 + 625 + 4 x}{2}, - \frac{25 + 625 + 4 x}{2}, \frac{25 - 625 + 4 x}{2}, - \frac{25 - 625 + 4 x}{2}

Find the domain of each inverse function

Domain of

\frac{25 + 625 + 4 x}{2} : x \geq - \frac{625}{4}

Domain of

- \frac{25 + 625 + 4 x}{2} : x \geq - \frac{625}{4}

Domain of

\frac{25 - 625 + 4 x}{2} : - \frac{625}{4} \leq x \leq 0

Domain of

- \frac{25 - 625 + 4 x}{2} : - \frac{625}{4} \leq x \leq 0

Combine the intervals

f (x) \geq - \frac{625}{4}

What is the range of f(x)=x^4-25x^2 ?
The range of f(x)=x^4-25x^2 is f(x)>=-625/4