In Exercises 55–58, find the indicated function values for each f...

Question

In Exercises 55–58, find the indicated function values for each function.____g(x) = −³√8x−8; g(2), g(1), g(0)

Accepted Answer

Welcome back. I am so glad you're here. And we are asked for the given values, find the value of F of X as indicated round the answer to two decimal places whenever necessary, the function that we're given. So F of X is equal to negative the cubed rut of 27 X -27. And the three values of F of X that we're asked to find are F of two s of one and F of zero. Our answer choices are answer choice A F of two is three F of one equals zero and F of zero equals negative three. Answer choice B F of two equals three F of one equals zero and F of zero equals three answer trace C F of two equals negative three F of one equals zero, F of zero equals negative three. And answer choice D F of two equals negative three, F of one equals zero and F of zero equals three. All right. Let's start off with F of two. So we're finding where X equals two, meaning that anywhere in our original equation where we had an X, we're going to plug in a two so we can bring down the rest, we have negative cubed root of 27. And here is the first X. So it's not 27 multiplied by X, it's 27 multiplied by two and then -27. So we do what's inside of the radical first, we'll take the multiplication 27 multiplied by two, which is 54. So we'll have the negative cubed rut of 54 -27. Now, with the order of operations, we continue doing the work inside of the radical 54 -27. Well, that equals 27. So we have the negative cube dr of 27. Now we can take the cube Dr of 27, the cube dr of 27 is three. So we bring down this negative and then we have a negative three. So F of two equals negative three. All right. Now we can do the work for F of one. So wherever we have an X in the original function, we are going to substitute now a one. So we have the negative cubed root of 27 not multiplied by X, but now multiplied by one minus 27. 27 multiplied by one is 27. So we have the negative cubed rut of 27 minus 27. Now we can do this subtraction 27 minus 27 is zero. So we have the negative cubed rut of zero while the cubed rot of zero is zero, negative zero is zero all around this just equals zero. So F of one equals zero. Now we can solve for F of zero. So at this point, wherever we have an X, we're going to substitute a zero. So we have the negative cubed Rutt of 27 multiplied by not X but zero minus 27. Well, do the multiplication 1st 27 multiplied by zero is zero. So we have the negative cubed root of zero minus 27 and doing the subtraction, 0 -27 is a -27. So we have the negative cubed of -27. We can take the cubed root of a negative number and the cubed re of -27 is -3. So we have a negative negative three. Well, taking a negative negative three gives us a positive three. So F of zero equals positive three. We look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.

In Exercises 55–58, find the indicated function values for each function.____g(x) = −³√8x−8; g(2), g(1), g(0)

Key Concepts

Cube Root Function

Function Evaluation

Algebraic Manipulation

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