Chapter 5: Q 10. (page 256)

Evaluate each expression using the graphs of $y = f (x)$ and $y = g (x)$ as shown in the given figure.
(a) $(g \circ f) (1)$ (b) $(g \circ f) (5)$ (c) $(f \circ g) (0)$ (d) $(f \circ g) (2)$ .

Short Answer

Expert verified

The value is (a) 3 (b) 4 (c) 1 (d) -2.

Step by step solution

Part (a) Step 1. Given information.

Evaluate each expression using the graphs of $y = f (x)$ and $y = g (x)$ .

Part (a) Step 2. Evaluation of a functional value.

The functional value is

$(g \circ f) (1) = g (f (1)) = g (- 1) = 3$ .

Part (b) Step 1. Given Information.

Evaluate each expression using the graphs of $y = f (x) & y = g (x)$ .

Part (b) Step 2. Evaluation of a functional value.

The functional value is

$(g \circ f) (5) = g (f (5)) = g (1) = 4$ .

Part (c) Step 1. Given Information.

Evaluate each expression using the graphs of $y = f (x) & y = g (x)$ .

Part (c) Step 2. Evaluation of a functional value.

The functional value is

$(f \circ g) (0) = f (g (0)) = f (5) = 1$ .

Part (d) Step 1. Given information.

Evaluate each expression using the graphs of $y = f (x) & y = g (x)$ .

Part (d) Step 2. Evaluation of a functional value.

The functional value is

$(f \circ g) (2) = f (g (2)) = f (2) = - 2$ .

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Evaluate each expression using the graphs of $y = f (x)$ and $y = g (x)$ as shown in the given figure.
(a) $(g \circ f) (1)$ (b) $(g \circ f) (5)$ (c) $(f \circ g) (0)$ (d) $(f \circ g) (2)$ .

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Evaluation of a functional value.

Part (b) Step 1. Given Information.

Part (b) Step 2. Evaluation of a functional value.

Part (c) Step 1. Given Information.

Part (c) Step 2. Evaluation of a functional value.

Part (d) Step 1. Given information.

Part (d) Step 2. Evaluation of a functional value.

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Evaluate each expression using the graphs of y=f(x)and y=g(x)as shown in the given figure.(a) g∘f1(b) g∘f5(c) f∘g0(d) f∘g2.

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Evaluation of a functional value.

Part (b) Step 1. Given Information.

Part (b) Step 2. Evaluation of a functional value.

Part (c) Step 1. Given Information.

Part (c) Step 2. Evaluation of a functional value.

Part (d) Step 1. Given information.

Part (d) Step 2. Evaluation of a functional value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Evaluate each expression using the graphs of $y = f (x)$ and $y = g (x)$ as shown in the given figure.
(a) $(g \circ f) (1)$ (b) $(g \circ f) (5)$ (c) $(f \circ g) (0)$ (d) $(f \circ g) (2)$ .