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Just need the answer for E!!!!
maths functions

Just need the answer for E!!!! maths functions-example-1
User Bill Keller
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1 Answer

15 votes
15 votes

Answer:
g(x) \ge f(x) for all x such that
x\le-2 or
x\ge0

Explanation:

This question is essentially asking at what x values would the graph of g(x) be greater than (higher than) or equal to f(x).

In the graph, we can see that g(x) is greater than (or higher than) f(x) at all x's before (to the left of) point E and after (to the right of) point A. An easy way to find the points E and A is by setting f(x) = g(x).


f(x)=g(x)\\1-x^2=2x+1\\1=x^2+2x+1\\0=x^2+2x\\0=x(x+2)\\x=0\hspace{0.1cm}or\hspace{0.1cm}x=-2

Since any value with x=-2 is left of the y-axis, we know that point E would have its x-coordinate as -2. Similarly, any point on the y-axis would have x=0; therefore, we can tell that point A would have its x-coordinate at 0.

If we remember that g(x) is greater than f(x) to the left of E and to the right of A, we can say that


g(x) \ge f(x) for all x such that
x\le-2 or
x\ge0

User Sukhbinder
by
3.3k points