Question

Prove that f(x) = 2x² + 3x - 5 is continuous at all points in R

Answer 1

f(x) = 2x² + 3x – 5

Clearly f(x) is defined for all points of R.

Let x₀ be an arbitrary point in R.

Then f(x₀) = 2x₀² + 3x₀ – 5   .......(1)

`lim_(x -> x_0) f(x) =  lim_(x -> x_0) (2x^2 + 3x - 5)`

= 2x₀² + 3x₀ – 5   .......(2)

From equation (1) and (2)

`lim_(x -> x_0) f(x) = f(x_0)`

Thus, f(x) is defined at all points of R limit of f(x) exist at all points of R and is equal to the value of the function f (x).

Thus f(x) is continuous at all points of R.