## Related questions with answers

Question

In this exercise, sketch the region bounded by the graphs of the algebraic functions and find the area of the region.

$f(x)=\sqrt{3x}+1,\quad g(x)=x+1$

Solutions

VerifiedSolution A

Solution B

Answered 2 years ago

Step 1

1 of 7In this task, we need to graph the region which is bounded by the given functions and determine its area.

Answered 2 years ago

Step 1

1 of 4The functions are

$\begin{aligned} & y = f(x) = \sqrt{3x}+1 \\[1ex] & y = g(x) = x+1 \end{aligned}$

We have plotted the required shaded area. Let us find out what are the intersection points.

$\begin{aligned} f(x) = g(x) & \implies \sqrt{3x}+1=(x+1) \\[1ex] & \implies \sqrt{3x}=x\\[1ex] & \implies 3x=x^2 \\[1ex] & \implies x(x-3)=0 \\[1ex] & \implies x=0,~\text{ or } x=3. \end{aligned}$

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