Question

1. consider the function f(x) = |x| + 2.
a) find f(-2), f(0), f(2), f(4).
b) Draw the graph of f (x).
c) write the domain and range of f(x).
d) write the range of the function g(x)=
|x|+5.
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Answer 1

Answer:

Solution : 

f(x)=x−2x−3f(x)=x-2x-3

Domain of f(x)f(x) will be any real number except 33 as x=3x=3 will make denominator 00.

∴∴ Domain =x∈R−{3}.x∈R-{3}.

To find range, we need to draw the graph of f(x).f(x).

Here, f'(x)=(3−x−x+2)(3−x)2=1(3−x)2f′(x)=(3-x-x+2)(3-x)2=1(3-x)2

∴f'(x)>0.∴f′(x)>0.

It means, graph of f(x)f(x) will always be increasing.

Now, we can draw the graph of f(x)f(x).

Please refer to the video to see the graph.

From the graph, we can see that f(x)f(x) goes from −∞→∞-∞→∞ except −1.-1.

∴∴ Range of f(x)f(x) will be (