Question

Helpppp me please!!!

Answer 1

To find the value of q, we need to find d(-8). Put another way, we need to find the value of d(x) when x = -8

$d(x) = -\sqrt{\frac{1}{2}x+4}$

$d(-8) = -\sqrt{\frac{1}{2}(-8)+4}$

$d(-8) = -\sqrt{-4+4}$

$d(-8) = -\sqrt{0}$

$d(-8) = 0$

So this means q = 0. Note that -0 is just 0.

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The value of r will be a similar, but now we use f(x) this time.

Plug in x = 0

$f(x) = \sqrt{\frac{1}{2}x+4}$

$f(0) = \sqrt{\frac{1}{2}*0+4}$

$f(0) = \sqrt{0+4}$

$f(0) = \sqrt{4}$

$f(0) = 2$

Therefore, r = 2.

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For s, we plug x = 10 into f(x)

$f(x) = \sqrt{\frac{1}{2}x+4}$

$f(10) = \sqrt{\frac{1}{2}*10+4}$

$f(10) = \sqrt{5+4}$

$f(10) = \sqrt{9}$

$f(10) = 3$

So s = 3.

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Finally, plug x = 10 into d(x) to find the value of t

$d(x) = -\sqrt{\frac{1}{2}x+4}$

$d(10) = -\sqrt{\frac{1}{2}(10)+4}$

$d(10) = -\sqrt{5+4}$

$d(10) = -\sqrt{9}$

$d(10) = -3$

A shortcut you could have taken is to note how d(x) = -f(x), so this means

d(10) = -f(10) = -9 since f(10) = 9 was found in the previous section above.

Whichever method you use, you should find that t = -3.

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In summary:

q = 0

r = 2

s = 3

t = -3