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2 years ago

Let f(x)=1/x+x, where is a nonzero number.what is the product of all the values of a, such that f(a)=f(2a)?

Mathematics

1 answer:

MAVERICK [17]2 years ago

3 0

The product of all the values of a, such that f(a)=f(2a) is -1/2

<h3>Functions and expressions</h3>

Given the function below;

f(x)=1/x + x

f(a) = 1/a + a

f(2a) = 1/2a + 2a

If f(a) = f(2a), hence;

1/a + a = 1/2a + 2a

Collect the like terms

1/a - 1/2a = 2a - a

2-1/2a = a

1/2a = a

Cross multiply

2a² = 1

a² = 1/2

a = ±√1/2

The values of a are √1/2 and -√1/2

Product = -√1/2 * √1/2

Product = -1/2

Hence the product of all the values of a, such that f(a)=f(2a) is -1/2

Learn more on functions here: brainly.com/question/25638609

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