Question

The set of values of 'a' for which the function f(x) = ax + b is strictly increasing for all real x, is _______________.

Answer 1

The given function is f(x) = ax + b.

f(x) = ax + b

Differentiating both sides with respect to x, we get

$f\text{'}\left(x\right)=a$

For f(x) to be strictly increasing for all real x,

$f\text{'}\left(x\right)>0$

$\Rightarrow a>0$

$\therefore a\in \left(0,\infty \right)$

Thus, the set of values of 'a' for which the function f(x) = ax + b is strictly increasing for all real x is (0, ∞).


The set of values of 'a' for which the function f(x) = ax + b is strictly increasing for all real x, is ____(0, ∞)____.