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Volgvan
3 years ago
6

Which answer describes the restrictions for the variables x+1/x-4?

Mathematics
2 answers:
MakcuM [25]3 years ago
5 0
The restriction for this is that x ≠ 4. This is because 4 - 4 = 0, and you cannot divide by zero.

An alternative way of writing this (interval notation) is (-∞, 4)U(4, <span>∞).

Hope this helps!</span>
vagabundo [1.1K]3 years ago
3 0
Hey there

<span>The restrictions for the variables x+1/x-4 is</span> x ≠ 4. 
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Let's create a table, and use arbitrary values of x between -3 and 3 (if the solution is not in this interval, we can use another one later). If we call:

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And now we can evaluate f(x) in each value of x to complete the table:

\begin{gathered} f(-3)=(-3)^2-4\cdot(-3)+4=9+12+4=25 \\ f(-2)=(-2)^2-4\cdot(-2)+4=4+8+4=16 \\ f(-1)=(-1)^2-4\cdot(-1)+4=1+4+4=9 \\ f(0)=0^2-4\cdot0+4=4 \\ f(1)=1^2-4\cdot1+4=1-4+4=1 \\ f(2)=2^2-4\cdot2+4=4-8+4=0 \\ f(3)=3^2-4\cdot3+4=9-12+4=1 \end{gathered}

The table is:

If we use this values and plot them in the cartesian plane.

We get:

And now if we plot a line that connects the points, we get the graph of the quadratic equation:

Since the problem ask us to find the value of x for which f(x) = 0, we can see both in the table and in the graph that this value is x = 2

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