For what value of λ is the function defined by
Continuous at x = 0? What about continuity at x = 1?

Question

For what value of λ is the function defined by Continuous at x = 0? What about continuity at x = 1?

Philoid · Accepted Answer

It is given that

It is given that f is continuous at x = 0, then, we get,

And

= 0

= 1

Thus, there is no value of for which f is continuous at x = 0

f(1) = 4x + 1 = 4 × 1 + 1 = 5

= 4 × 1 + 1 = 5

Then,

Hence, for any values of, f is continuous at x = 1