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.
___
f(x) = ³√x−1; f(28), f(9), f(0), f(−63)

Accepted Answer

Welcome back. I am so glad you're here. We are asked for the given values, find the value of F of X as indicated round the final answer to two decimal places. Whenever necessary, the function that we're given is F of X equals the cubed rut of X -4. And the four different values that were asked to find are F of s of s of negative four and F Of -23. And our answer choices are answer choice A F of 68 equals five F of 129 equals four, F of negative four equals negative three and F of negative 23 equals negative two. Answer. Choice B is that F of 68 equals five F of 129 equals four F of negative four equals negative two and F of negative 23 equals negative three. Answer. Choice C is that F of 68 equals four F of 129 equals five F of negative four equals negative three and F of negative 23 equals negative two. And answer choice D is that F of 68 equals four F of 129 equals five F of negative four equals negative two and F of negative 23 equals negative three. All right. So for the first one, for F of 68, that means that wherever we had an X in our original function, we are substituting a 68. So we'll have F of 68 equals the cubed root of and there's our X. So instead of X, we'll have 68 and then bring over the -4. So now we do what's inside of the radical first. So we take 68 -4, which equals 64. So we have the cubed rut of 64 and the cubed root of 64 or what multiplied by what multiplied by what or what multiplied by itself three times equal 64. That is four. So F of 68 equals 4. Now let's work on F of 129. So where we had an X in the original function, we are now substituting 129. So we'll take the cube dr of not X but 129 minus four, doing the subtraction inside the radical. 1st. 129 -4 is 125. So we have the cubed root of 125. The cubed rot of 125 is a positive five. So F of 129 equals 5. Now let's work on F of -4. Now substituting a negative four wherever we had an X in the original function. So F of negative four equals the cube dr of not X but negative four minus four, negative four minus four equals negative eight. So we have the cubed rut of negative eight, we can take the cubed rut of a negative number. And what multiplied by what multiplied by what gives us a negative eight. That's going to be a negative two. So F of negative four equals negative two. Now, the final one here will take F of -23 substituting a negative 23 in for X. So we take the cube dr of not X but negative 23 minus four, -23 -4 is -27. So we have the cube threat of negative 27 and the cube dr of -27 is -3. All right. So we're looking for F of 68 equals four, F of 129 equals five. F of negative four equals negative two and F of negative equals negative three which matches 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. ___ f(x) = ³√x−1; f(28), f(9), f(0), f(−63)

Key Concepts

Cube Root Function

Function Evaluation

Domain of the Function

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