Let ƒ(x) = 1/ (x³+1).
Compute ƒ(2) and ƒ(y²).

Question

Let ƒ(x) = 1/ (x³+1).

Compute ƒ(2) and ƒ(y²).

Accepted Answer

Welcome back everyone. In this problem, we want to calculate g of 3 and g of zed cubed for the function g of x equals 1 divided by x squared plus 5. For our answer choices, a says Jeff 3 is 14 and Jeff Z cubed is zed to the 6th power plus 5. B says Jeff 3 is 8 and Jeff Z cubed is zed cubed plus 5. C says G of 3 is an 8 and G of Z cubed is 1 divided by the expression Z cubed plus 5. And this says G of 3 is 1 14th and g of zed cubed is 1 divided by the expression zed to the power of 6 plus 5. Now if we're going to solve for g of 3, what that means is that we're going to put the value 3 as our input into the function g of x. Given g of x equals 1 divided by x squared plus 5, it means that anywhere we see our input x, we're going to put the value 3 for g of 3. So that tells us then that g of 3 equals 1 divided by 3 squared plus 5. 3 squared is 9 and 9 +5 equals 14. Hence, g of 3 equals 1 14th. Next, let's try to find g of zed cubed. The same idea applies. Now anywhere we see x, we're going to put zed cubed. So that means our function is going to be 1 divided by zed cubed squared plus 5. Now in this expression, we're raising a power to a power and recall that when we raise a power to a power, we multiply the powers. So a to the power of b raised to the power of c is the same thing as saying a to the power of b multiplied by c. We can apply that idea here because then that tells us that z cubed raised to the power of 2 is really z to the power of 3 multiplied by 2. 3 multiplied by 2 equals 6. So our answer would be zed 1 divided by the expression zed to the power of 6 plus 5. Thus, g of 3 equals 1 14th and g of zed cubed equals equals 1 divided by the expression zed to the power of 6 plus 5. And when we look back in our answer choices, that would have been answer choice d. Thanks a lot for watching everyone. I hope this video helped.

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Let ƒ(x) = 1/ (x³+1).
Compute ƒ(2) and ƒ(y²).

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

Let ƒ(x) = 1/ (x³+1).Compute ƒ(2) and ƒ(y²).

Let ƒ(x) = 1/ (x³+1).
Compute ƒ(2) and ƒ(y²).