Let

Question

Let $g\left(x\right)=\frac{x^3-4x}{8\left|x-2\right|}$ .

Calculate $g\left(x\right)$ for each value of $x$ in the following table.

Accepted Answer

Welcome back everyone. In this problem, we want to evaluate F of X equals X cubed minus 25 X divided by 125 multiplied by the absolute value of X minus five for all values of X in the table and rounded to five decimal places. Here we have our table and for our answer choices, we have tables full of possible values for X and F of X for the given values for X. Now to evaluate the function, all we need to do is to plug in the respective values of X into F FX to help us solve. So let's go ahead and try to do that. OK? So let's start at X equals 4.9. Now, when X equals 4.9 OK, then F of 4.9 is going to be equal to 4.9 cubed minus 25 multiplied by 4.9. And this is gonna be divided by 125 multiplied by the absolute value of 4.9 minus five. Now, we could work this out here. But in the interest of time when you go ahead and substitute these values into our expression for F of X, it eventually works out that F of 4.9 is equal OK to negative 0.38808. OK. So that's the value of F of 4.9. So we can put that value into our table. Now, essentially what we are going to do is to substitute the rest of these values in the same way to solve for the rest of values for F FX again because of the time I won't be able to go through each one individually. But while solving, you should find that you get F of 4.99 to be equal to negative 0.39880 you should get F of 4.999 to be equal to negative 0.39988. And you should get F of 4.9999 to be equal to negative 0.39999. OK? So we can take those values and put them into our table 9999. Now we're going to do the same for the values of X below. OK? 5.15 0.01. And so on. Now when you substitute 5.1 into the function, you should get F FX to be 0.41208 at X equals 5.01. Then F FX equals 0.40120 at F of 5.001 F FX equals 0.40012. And at X equals 5.0001 F of X equals 0.40001. OK? So now again, let's go back to our table. We're gonna put those values in 0.412080 0.401200 0.40012 and 0.40001. So now these are going to be all the values for F of X for our changing values of X. Now, if we compare our answer to the tables in our answer choices, then you should find that A is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

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Calculate $g\left(x\right)$ for each value of $x$ in the following table.

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Let $g\left(x\right)=\frac{x^3-4x}{8\left|x-2\right|}$ . <IMAGE>
Calculate $g\left(x\right)$ for each value of $x$ in the following table.