SECTION A Question one (a) If f(x) = x²+ find the range under the function when the domain is −2≤x≤5 (b) Given the functions f(x) = 2x+3,g(x) = 3x + 3 and h(x) = evaluate the following

The function $f(x) = x^2 + \frac{1}{2}$ is a parabola opening upwards. Its vertex is at $(0, \frac{1}{2})$. Since $x=0$ is within the given domain $[-2, 5]$, the minimum value of $f(x)$ will occur at $x=0$.

Substitute $x=0$ into the function:

The minimum value of $f(x)$ is $\frac{1}{2}$.

Substitute $x=-2$ and $x=5$ into the function:

Comparing the values $\frac{1}{2}$, $\frac{9}{2}$, and $\frac{51}{2}$, the maximum value of $f(x)$ in the given domain is $\frac{51}{2}$.

The range of the function for the given domain is the interval from the minimum value to the maximum value.
The range is $\left[\frac{1}{2}, \frac{51}{2}\right]$.

The final answer is $\boxed{\left[\frac{1}{2}, \frac{51}{2}\right]}$.