Chapter 10: Q. 10 (page 1002)

For functions $f (x) = 5 x^{2} - 1$ and
$g (x) = 4 x - 1$ find
a. $f \circ g (1)$
b. $g \circ f (- 1)$
c. $f \circ f (2)$

Short Answer

Expert verified

The value is $44, 15, 1804$ respectively

Step by step solution

Given information

Given the function

$f (x) = 5 x^{2} - 1 g (x) = 4 x - 1$

Calculate g(1) by substituting in g(x)

Substituting, $x = 1$ , we get

role="math" localid="1644935694008" $g (1) = f (4 x - 1) g (1) = f (4 (1) - 1) g (1) = f (3)$

Calculate f(3) by substituting in the function

Substituting , we get

$f (3) = 5 x^{2} - 1 f (3) = 5 {(3)}^{2} - 1 f (3) = 44$

Calculate f(-1) by substituting in the value

Substituting, we get

$f (- 1) = 5 {(- 1)}^{2} - 1 f (- 1) = 5 - 1 f (- 1) = 4$

Calculate g(4) by substituting the value in the function

Substituting the values, we get

$g (4) = 4 x - 1 g (4) = 4 (4) - 1 g (4) = 15 g \circ f (- 1) = 15$

Step 6:Substitute f(2) by substituting in the values

Substituting, we get

$f (2) = 5 x^{2} - 1 f (2) = 5 {(2)}^{2} - 1 f (2) = 19$

Calculating f(19) by substituting in the values

Substituting the values, we get

$f (19) = 5 x^{2} - 1 f (19) = 5 {(19)}^{2} - 1 f (19) = 1804$

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For functions $f (x) = 5 x^{2} - 1$ and
$g (x) = 4 x - 1$ find
a. $f \circ g (1)$
b. $g \circ f (- 1)$
c. $f \circ f (2)$

Short Answer

Step by step solution

Given information

Calculate g(1) by substituting in g(x)

Calculate f(3) by substituting in the function

Calculate f(-1) by substituting in the value

Calculate g(4) by substituting the value in the function

Step 6:Substitute f(2) by substituting in the values

Calculating f(19) by substituting in the values

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For functions f(x)=5x2-1and g(x)=4x-1finda.f∘g(1)b.g∘f(-1)c.f∘f(2)

Short Answer

Step by step solution

Given information

Calculate g(1) by substituting in g(x)

Calculate f(3) by substituting in the function

Calculate f(-1) by substituting in the value

Calculate g(4) by substituting the value in the function

Step 6:Substitute f(2) by substituting in the values

Calculating f(19) by substituting in the values

One App. One Place for Learning.

Most popular questions from this chapter

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Discrete Mathematics

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

For functions $f (x) = 5 x^{2} - 1$ and
$g (x) = 4 x - 1$ find
a. $f \circ g (1)$
b. $g \circ f (- 1)$
c. $f \circ f (2)$