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mamaluj [8]
3 years ago
14

I need help with solving this question with the steps

Mathematics
1 answer:
nasty-shy [4]3 years ago
6 0

we are given

f(x)=\frac{x^2+5x+6}{x+3}

Firstly , we will factor numerator numerator

f(x)=\frac{(x+3)(x+2)}{x+3}

we can see that both numerator and denominator has common term as x+3

so, there will be hole at x+3=0

and we know that hole is a type of discontinuity

so, discontinuity would be at

x=-3............Answer

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What is the inverse equation of the function, y = 3x - 6?
algol [13]
The best answer (and only correct answer) among the answer choices given is:
________________________________________________
                    [C]:    y⁻¹ = (x+6) / 3  .
_________________________________________________
Explanation:
__________________________________________________
 Given the original function:  y = 3x - 6 ;
_________________________________________________
To find the "inverse equation" of said function; we change the "x" to a y"; and the "y" to an "x"; and rewrite:
_________________________________________________
x = 3y <span>− 6 ; 

Now, rewrite in "slope-intercept form" ; or y = mx + b ;
     that is, with y as "single, isolated" variable on the left-hand side of the equation (with an "implied coefficient of positive one", only);  then an "equal sign, then "mx + b" ; in which: "m" is the coefficient of the variable, "x"; and in which "m" refers to the "slope";  and "b" refers to the 'y-intercept".
_____________________________________
So,we have the inverse function: 
____ </span>_________________________________________________
      x = 3y − 6  ;  we want to write in slope-intercept form; 
__________________________________________________
Add   "6" to each side of the equation:
__________________________________
     x + 6 = 3y − 6 + 6 ; 
__________________________________
 x + 6 = 3y ;  
________________________
 ↔ Rewrite as:   3y = x + 6 ; 
________________________________________
 Divide EACH side of the equation by "3" ; to isolate "y" one side of the equation; specifically, the left-hand side of equation; and to write in "slope-intercept form:
______________________________
              3y / 3 = (x + 6) / 3  ;
______________________________
   to get:
______________________________
                  y = (x + 6) / 3 ; 
_________________________________
                 y = (x/3)  + (6/3) ;
____________________________________
                y = (x/3 ) + 2 ;
___________________________________
or;  write as: y = (1/3)x + 2 ;
________________________________________
Now, let us examine the answer choices given:
__________________________________________
Note that all the answer choices begin with "y-1" ;
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__________________________________________________
That being said, we can write the aforementioned "rewritten equations" (see above in THIS VERY ANSWER) as:
_____________________________________
y⁻¹ = (x + 6) / 3 ; 
_________________________________
                 y⁻¹ = (x/3)  + (6/3) ;
____________________________________
                y⁻¹ = (x/3 ) + 2 ;
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or;  write as: y⁻¹ = (1/3)x + 2 
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That being said:
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The best answer (and only correct answer) among the answer choices given is:  Answer choice: [C]:  y⁻¹ = (x+6) / 3  .
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