Answer to Question #229999 in Algebra for grilo

Question

calculate where f(x)=g(x)from your graph and hence solve the inequality

Answer 1

This question is incomplete but we can take an example as per the question asked.

Let $f(x)=x^2, g(x)=x$

On plotting these on the graph, we get

From the graph, $f(x)=g(x)$ will obtained where these two curves intersect each other.

So, $f(x)=g(x)$ at $(0,0)$ and $(1,1)$ i.e., at $x=0, y=0$ and at $x=1, y=1$ .

Now, for $f(x)>g(x)$

$\Rightarrow x^2>x \\\Rightarrow x^2-x>0 \\\Rightarrow x(x-1)>0 \\x\in(-\infty,0)\cup(1,\infty)$

Now, for $f(x)<g(x)$

$\Rightarrow x^2<x \\\Rightarrow x^2-x<0 \\\Rightarrow x(x-1)<0 \\x\in(0,1)$