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Click here please. The problems are in picture format

Click here please. The problems are in picture format-example-1
Click here please. The problems are in picture format-example-1
Click here please. The problems are in picture format-example-2
User Janette
by
8.3k points

1 Answer

3 votes

First picture:

You got the first two right (good job!), so I'll just tackle the third one. If you have to compute
f(x-4), it means that you have to substitute
x-4 in place of
x. Differently from the first two points, this will generate a new function, rather than a specific value:


f(x) = √(x+4)+2 \implies f(x-4) = √((x-4)+4)+2 = √(x)+2

Second picture:

Given the point
(x,y) highlighted in the picture, you can deduce that the base is
2x units long (since it spans from
(-x,0) to
(x,0)) and the height is
y units long (because it spans from
(x,0) to
(x,y)). So, the area of the rectangle is the multiplication between base and height:


A = 2xy

But we know that
y=f(x)=√(36-x^2), so we have


A = 2x√(36-x^2)

The domain of this function is given by the domain of the square root: we want its argument to be non, negative, so we have


36-x^2 \geq 0 \iff x^2 \leq 36 \iff -6 \leq x \leq 6

But since the problem is symmetric, the answer is


0 \leq x \leq 6

You can only see the answer
0 < x < 6 because, if you choose
x=0 or
x=6, the rectangle degenerates to a segment, and your exercise doesn't like this scenario, apparently

User Seema
by
7.9k points

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