Composition of even and odd functions from graphs

Question

Composition of even and odd functions from graphs Assume ƒ is an even function and g is an odd function. Use the (incomplete) graphs of ƒ and g in the figure to determine the following function values. <IMAGE>

e. g(g(-7))

e. g(g(-7))

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. The graphs of U of X and VFX are shown in the following image where U of X is an even function and V of X is an odd function. Find the value of V of -6. Awesome. So it appears the final answer that we're ultimately trying to solve for is we're trying to figure out this function within a function. So we're trying to figure out V of V-6. Awesome. So with that in mind, let's quickly look at our graph that is provided to us by the prom itself, and as you can see, we have two different curves. We have our red curve, which is denoting our UFX function, which is even. And we have a green curve which is denoting our VFX function, which is odd, and it appears from our graph that they both start from the origin point, which is 0.0. So they both start from 00. Awesome. So now that we have a visualization of what's going on for this particular problem, let's read off our multiple choice answers to see what our final answer might be. A is 3, B is -3. C is 4 and D is -4. OK. So first off, in order to solve this problem, we need to focus our attention on our VFX function. So we need to remember once again that VFX is equal to our odd function, which I put in O in quotation marks to mean odd. And because VF X is an odd function, you can go ahead and safely write that V-6, so V-6 is the same as it's equal to negative. V of 6, so, once again, V-6 is equal to negative V6 and referring to our graph when we solve for V of 6, so V 6 is equal to 3. Awesome, so we can therefore as a result, write that. V-6, so V-6 is equal to negative V6, which is equal to -3. So we can take it a step further and write that V of V of -6. is going to be equal to V of -3, and we need to recall from our graph that V of -3 is equal to negative V3. So, from the graph, we could state that V of 3 is equal to 4. And V of -3 is equal to negative of 3, which is equal to -4. So that will mean without a doubt that V of V-6 is equal to -4, and that is our final answer. Hooray, we did it. And this corresponds with multiple choice answer letter D, which once again is -4. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Composition of even and odd functions from graphs Assume ƒ is an even function and g is an odd function. Use the (incomplete) graphs of ƒ and g in the figure to determine the following function values. <IMAGE>

e. g(g(-7))

Key Concepts

Even Functions

Odd Functions

Function Composition

Watch next

Composition of even and odd functions from graphs Assume ƒ is an even function and g is an odd function. Use the (incomplete) graphs of ƒ and g in the figure to determine the following function values. <IMAGE>e. g(g(-7))

Key Concepts

Even Functions

Odd Functions

Function Composition

Watch next

Composition of even and odd functions from graphs Assume ƒ is an even function and g is an odd function. Use the (incomplete) graphs of ƒ and g in the figure to determine the following function values. <IMAGE>

e. g(g(-7))