Chapter 10: Q 10.4TI (page 992)

$For functions f (x) = x^{2} + 1, and g (x) = 3 x - 5, find (A) (f \circ g) ⎠ (- 1), (B) (g \circ f) (2), and (C) (f \circ f) (- 1) .$

Short Answer

Expert verified

Part(a) 63

Part(b) -14

Part(c) 5

Step by step solution

Step 1. Given information

Find

f (x) = x^{2} + 1, and g (x) = 3 x - 5, find (A) (f \circ g) ⎠ (- 1), (B) (g \circ f) (2), and (C) (f \circ f) (- 1) .

Part(a)Step 2. Calculation

$\begin{array}{l} Use the definition of (f \circ g) (- 1) . & (f \circ g) (- 1) = f (g (- 1)) \\ Find g (- 1) where g (x) = 3 x - 5 . & (f \circ g) (- 1) = f (3 \cdot (- 1) - 5) \\ Simplify. & (f \circ g) (- 1) = f (- 8) \\ Find f (- 8) where f (x) = x^{2} + 1 . & (f \circ g) (- 1) = (- 8)^{2} - 1 \\ Simplify. & (f \circ g) (- 1) = 63 \end{array}$

Part (b) Step 3. Calculation

$\begin{array}{l} Use the definition of (g \circ f) (2) . & (g \circ f) (2) = g (f (2)) \\ Find f (2) where f (x) = x^{2} + 1 . & (g \circ f) (2) = g ((2)^{2} + 1) \\ Simplify. & (g \circ f) (2) = g (5) \\ Find g (5) where g (x) = 3 x - 5 . & (g \circ f) (2) = 3 (- 3) - 5 \\ Simplify. & (g \circ f) (2) = - 14 \end{array}$

Part(c)Step 4. Calculation

$\begin{array}{l} Use the definition of (f \circ f) (- 1) . & (f \circ f) (- 1) = f (f (- 1)) \\ Find f (2) where f (x) = x^{2} + 1 . & (f \circ f) (- 1) = f ({(- 1)}^{2} + 1) \\ Simplify. & (f \circ f) (- 1) = f (2) \\ Find f (2) where f (x) = x^{2} + 1 . & (f \circ f) (- 1) = 2^{2} + 1 \\ Simplify. & (f \circ f) (- 1) = 5 \end{array}$

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$For functions f (x) = x^{2} + 1, and g (x) = 3 x - 5, find (A) (f \circ g) ⎠ (- 1), (B) (g \circ f) (2), and (C) (f \circ f) (- 1) .$

Short Answer

Step by step solution

Step 1. Given information

Part(a)Step 2. Calculation

Part (b) Step 3. Calculation

Part(c)Step 4. Calculation

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Forfunctionsf(x)=x2+1,andg(x)=3x−5,find(A)(f∘g)⎠(−1),(B)(g∘f)(2),and(C)(f∘f)(−1).

Short Answer

Step by step solution

Step 1. Given information

Part(a)Step 2. Calculation

Part (b) Step 3. Calculation

Part(c)Step 4. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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$For functions f (x) = x^{2} + 1, and g (x) = 3 x - 5, find (A) (f \circ g) ⎠ (- 1), (B) (g \circ f) (2), and (C) (f \circ f) (- 1) .$