# Continuity Theorems – Intermediate value theorem – Exercise 1033

Exercise

The function

$$f(x)$$

Is continuous for all real numbers and the following holds

$$\lim _ { x \rightarrow \infty}f(x)=-7$$

$$f(2)=5$$

Prove that there is at least one point, which holds

$$f(a)=a$$

Proof

Coming soon

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