Question

determine that wheter the functions from real numbers to real numbers are one to one
f(n)=n^3
f(n)=n^2+1

Answer 1

Answer on Question #83062 – Math – Discrete Mathematics

Question

determine that whether the functions from real numbers to real numbers are one to one

f(n)=n^3

f(n)=n^2+1

Solution

If the statement $f(a) = f(b)$ implies $a = b$, then the function $f(x)$ is one to one.

We apply this test to check the function $f(n) = n^3$:

$$a^3 = b^3$$ $$a = b$$

Therefore $f(n) = n^3$ is one to one.

We apply this test to check the function $f(n) = n^2 + 1$:

$$a^2 + 1 = b^2 + 1$$ $$a^2 = b^2$$ $$a = b \quad \text{or} \quad a = -b$$

Therefore $f(n) = n^2 + 1$ is not one to one.

Answer:

$f(n) = n^3$ is one to one.

$f(n) = n^2 + 1$ is not one to one.

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