Question

examine the continuity f(x)=x-5​

Answer 1

Answer:

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Answer 2

$\huge\orange {\boxed {\mathfrak {Solution}}}$

$f(x) = x - 5 \\ x - 5 \: \: is \: a \: polynomial \\ x = c \\ f(x) \: \: is \: continuous \: at \: x = cf \\ limf(x) = f(c) \\ lim \: f(x) = lim \: x - 5 \\ = c - 5 \\ \\ f(c) = c - 5 \\ \\ \\ \\ \\ \\ \\ \\ since \: \: \: lim \: f(x) = f(c) \\ \\ f \: is \: continuous \: for \: x = c \\ where \: c \: is \: a \: real \: number$

Therefore, f is continuous for all real numbers.

Hence , f is continuous for each x € R