$\"\"$

The condition are :

$\"\"$ , $\"\"$ .

$\"\"$ and $\"\"$ for all $\"\"$ .

(a)

Graph :

Graph the function such that all the conditions are satisfied :

Since $\"\"$ , so the function is increasing function.

$\"\"$ represents that $\"\"$ is increasing for all vales of $\"\"$ .

$\"\"$ represents that $\"\"$ is concave downward for all vales of $\"\"$ .

$\"\"$

(b)

Observe the graph.

The function is increasing function.

Therefore the function touches the $\"\"$ -axis atmost once.

The function $\"\"$ has only one solution.

$\"\"$

(c)

$\"\"$ and $\"\"$ .

As the function increases, slope is decreases.

$\"\"$ .

$\"\"$ is not possible for the solution.

$\"\"$

(a) Graph the function is drawn such that all the conditions are satisfied is

$\"\"$

(b) The function $\"\"$ has only one solution.