What is the range of f(x)= 1/(x^2-10x+25) ?

The range of f(x)= 1/(x^2-10x+25) is f(x)>0

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range of f(x)= 1/(x^2-10x+25)

range

f (x) = \frac{1}{x ^{2} - 10 x + 25}

f (x) > 0

Interval Notation

(0, \infty)

Solution steps

Rewrite as

\frac{1}{x ^{2} - 10 x + 25} = y

Multiply both sides by

x^{2} - 10 x + 25

1 = y (x^{2} - 10 x + 25)

The range is the set of y for which the discriminant is greater or equal to zero

Discriminant

1 = y (x^{2} - 10 x + 25) : 4 y

4 y \geq 0 : y \geq 0

Check if the range interval endpoints are included

y = 0 :

Excluded

Therefore the range is

f (x) > 0

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

f (x) = (x - 7)^{2}

y = - x^{2} + 7 x + 1

2 cos (x) - sin (2 x)

f (x) = \frac{4}{x + 6}

What is the range of f(x)= 1/(x^2-10x+25) ?
The range of f(x)= 1/(x^2-10x+25) is f(x)>0