Let f and g be defined by the following table: Find

Question

\sqrt{f (- 1) - f (0)} - [g (2)]^{2} + f (- 2) \div g (2) \cdot g (- 1) .

Accepted Answer

Welcome back. I'm so glad you're here. We have this data table and we're to use it to solve the given expression. Look at this expression oh my goodness. It's the square root of F. Of one squared plus G. Of negative two squared divided by G. Of one plus F. Of negative two times G of zero. Alright, we got this. Let's start finding our values in our table. The first one here half of one. That means we're going to look at the F. Of X. Row and then we're going to find the column that has the X. Value of one. And that's going to be this spot right here. So our value for half of one is three. And it's very important. Don't forget to square that because of that little squared up by R. F. Okay now let's look for G of negative two. So the G. Of X. Row and the column that has the X. Value of negative two. That's going to be right here, negative four. So that'll be a three squared plus a negative four. Also squared divided by G. Of one. Let's find that. That's the G. Of X row and the column where X equals one. That's right here, that's negative one. So negative one. In our denominator plus F. Of negative two. Alright. F. Of X. Row and the column where X equals negative two. That's here. Nine and R. G of zero. Okay, that's the G of X. Row and the column or X equals zero. That's going to be a negative two. So nine times negative two. Okay let's do the math. So in the numerator here we've got the square root of three squares nine plus negative four squared is 16 divided by negative one plus nine times negative two is negative 18. In the numerator. The square root of nine plus 16 is the square root of 25. Divided by negative one plus a negative 18. Continuing down here, the squirt of 25. That's five divided by negative one plus a negative 18. Simplifying five divided by negative one. That's negative five plus a negative 18 adding those two negative numbers together. We get negative 23. We look at our answer choices and that matches with answer choice. C Well done. We'll catch on the next one.

Let f and g be defined by the following table: Find $\sqrt{f (- 1) - f (0)} - [g (2)]^{2} + f (- 2) \div g (2) \cdot g (- 1) .$

Key Concepts

Function Evaluation

Order of Operations

Square Root and Exponents

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