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Ymorist [56]
3 years ago
11

H(x)= ⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎧ ​ 8+6x x+4 10 ​ 4x−3 ​ , , , ​ x<−7 −7≤x<−5 x≥−5 ​

Mathematics
1 answer:
motikmotik3 years ago
4 0

Answer:

h(-6) = -\frac{1}{5}

Step-by-step explanation:

Given

h(x) =\left[\begin{array}{cc}8 + 6x\ \ &x < -7\\\frac{x + 4}{10} &-7 \le x

Required

Determine h(-6)

To do this, we make use of:

h(x) = \frac{x + 4}{10}

Because -7 \le -6

So, we have:

h(x) = \frac{x + 4}{10}

h(-6) = \frac{-6 + 4}{10}

h(-6) = \frac{-2}{10}

Simplify

h(-6) = -\frac{1}{5}

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where x is nonzero

=======================================================

Explanation:

We'll use two rules here

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------------------------------

The portion [ x^(a-b) ]^(a+b) would turn into x^[ (a-b)(a+b) ] after using the first rule shown above. That turns into x^(a^2 - b^2) after using the difference of squares rule.

Similarly, the second portion turns into x^(b^2-c^2) and the third part becomes x^(c^2-a^2)

-------------------------------

After applying rule 1 to each of the three pieces, we will have 3 bases of x with the exponents of (a^2-b^2),  (b^2-c^2) and (c^2-a^2)

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