Answer:
Step-by-step explanation:
We can use the definition of inverse functions. Recall that if two functions, <em>f</em> and <em>g</em> are inverses, then:
So, we can let <em>j</em> be the inverse function of <em>h</em>.
Function <em>h</em> is given by:
Find its inverse. Flip variables:
Solve for <em>y. </em>Add:
Hence:
Therefore, <em>a</em> = 1/3 and <em>b</em> = 2/3.
We can verify our solution:
And:
<u>Let's take this problem step-by-step</u>:
<u>Let's first set up some variables</u>:
<u>Let's examine the information given:</u>
⇒ average child is 75 pounds
⇒ average adult is 150 pounds
⇒<em> therefore</em>:
⇒ <em>therefore</em>:
<u>Let's graph the equations</u>:
⇒ look at the image attached
<u>The point at which the two graphs intersect:</u>
⇒ <em>is the solution that represents the amount of children and adults and </em>
<em> their combine weight</em>
<em />
<u><em>With the horizontal axis being the # of children and vertical axis being the # of adults</em></u><em>:</em>
<em> ⇒ the </em><em>solution is 8 children and 6 adults</em>
<em></em>
<u>Answer: 8 children and 6 adults</u>
<u></u>
Hope that helped!
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