Suppose f has the intermediate value property on an interval I and let k be a constant. Prove that kf has the intermediate value property.
The Attempt at a Solution
Since f has IVP on I, then there is distinct a and b in I and f(c)=v exists and is between f(a) and f(b).
Let k be a constant real number.
Then kf(a), kf(b) and kf(c) are all real numbers where kf(c) is between kf(a) and kf(b) by properties of real numbers.
So then kf has IVP on I?