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Standard XII

Mathematics

Linear Functions

Let f:ℝ→ℤ be ...

Question

Let $f : R \to Z$ be a continuous function such that $f (4) = 4$ . Then the value of $f (5)$ is

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Solution

Since $f$ is a continuous function and range is integer, so $f (x)$ is a constant function.
As $f (4) = 4$ , so
$f (x) = 4$ for all $x \in R$
$∴ f (5) = 4$

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Linear Functions

Standard XII Mathematics

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Let f:R→Z be a continuous function such that f(4)=4. Then the value of f(5) is

Since f is a continuous function and range is integer, so f(x) is a constant function. As f(4)=4, so f(x)=4 for all x∈R ∴f(5)=4

Let $f : R \to Z$ be a continuous function such that $f (4) = 4$ . Then the value of $f (5)$ is

Since $f$ is a continuous function and range is integer, so $f (x)$ is a constant function.
As $f (4) = 4$ , so
$f (x) = 4$ for all $x \in R$
$∴ f (5) = 4$