Use the graph of ƒ to find 

Question

Use the graph of ƒ to find ƒ⁻¹ (2),ƒ⁻¹ (9), and ƒ⁻¹ (12)

Accepted Answer

Welcome back, everyone. Find G inverse at points -7, 3, and 9 using the graph of G. For this problem, let's recall a sy property. If we have a parent function G of X, and if we take G at point of its inverse G inverse of X. We simply get the independent variable itself, which is X. Soon we will understand why this is useful. For example, let's take G in versa. -7, right? And let's substitute it into the formula. If we take G at G inverse of 7, well, we are going to get -7. And if we look at this expression, let's suppose that G inverse at -7 is simply a variable n. So we are looking at an expression of G N is equal to -7. So N is the X value, and then the Y value is -7. If we identify the X value at which G is equal to -7, well, that x value is going to give us the required answer. So what we have to do is basically look at the graph and identify -7 on the vertical axis. And then we want to identify the X value which corresponds to the Y value of -7. We can see that the X value is also -7 and that X value is the required N, right? So we can say that N is equal to -7 and that N is. G in verse at. -7. Well then, we have our first answer, G inverse at.-7 is equal to -7. Let's continue using the same method. Now we want to evaluate G inverse at 0.-3 so if we take G of G inverse at 0.3 we're going to get 3. We're going to get negatives. I'm sorry, right? So now we have a Y value. Of -3, we want to locate it in the given graph. And now, let's identify the X value, which corresponds to the Y value of -3 on the graph of G. We can see that the X value is going to be equal to -2. So G inverse at 0.3 is equal to -2. Similarly, if we want to identify G inverse at 0.9, we take G at G inverse of 9. Based on the given property, this must be equal to 9. So now the y value of G is equal to 9. Let's label it on the graph, and we simply want to identify the X value at which G is 9. If we look at the given graph, the X value at which G is equal to 9 is also 9. So we can see that G inverse at 0.9 is equal to 9. And we have our final answers. Thank you for watching.

Use the graph of ƒ to find ƒ⁻¹ (2),ƒ⁻¹ (9), and ƒ⁻¹ (12) <IMAGE>

Key Concepts

Inverse Functions

Graph Interpretation

Function Notation

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