Chapter 2: Q. 42 (page 69)

In Problems 39– 46, find the following for each function:
$(a) f (0) (b) f (1) (c) f (- 1) (d) f (- x) (e) - f (x) (f) f (x + 1) (g) f (x) (h) f (x + h)$
$f (x) = \frac{x^{2} - 1}{x + 4}$

Short Answer

Expert verified

The value of

f (0) = \frac{- 1}{4} f (1) = f (- 1) = 0 f (- x) = \frac{x^{2} - 1}{4 - x} - f (x) = \frac{1 - x^{2}}{x + 4} f (x + 1) = \frac{x (x + 2)}{x + 5} f (x) = \frac{x^{2} - 1}{x + 4} f (x + h) = \frac{{x^{2} + 2 x h + h}^{2} - 1}{x + h + 4}

Step by step solution

Step 1. Given Information

$(a) f (0) (b) f (1) (c) f (- 1) (d) f (- x) (e) - f (x) (f) f (x + 1) (g) f (x) (h) f (x + h)$

$f (x) = \frac{x^{2} - 1}{x + 4}$

Part (a) Step 1. We find the value of f(0)Putting x=0 in the given question.

$f (0) = \frac{{(0)}^{2} - 1}{0 + 4} f (0) = \frac{- 1}{4}$

Part (b) Step 1. We find the value of f(1)Putting x=1 in the given question.

$f (1) = \frac{{(1)}^{2} - 1}{1 + 4} f (1) = \frac{1 - 1}{5} f (1) = \frac{0}{5} f (1) = 0$

Part (c) Step 1. We find the value of f(-1)Putting x=-1 in the given question.

$f (- 1) = \frac{{(- 1)}^{2} - 1}{- 1 + 4} f (- 1) = \frac{1 - 1}{3} f (- 1) = \frac{0}{3} f (- 1) = 0$

Part (d) Step 1. We find the value of f(-x)Putting x=-x in the given question.

$f (- x) = \frac{{(- x)}^{2} - 1}{- x + 4} f (- x) = \frac{x^{2} - 1}{4 - x}$

Part (e) Step 1. We find the value of -f(x)To find the value we multiply the given equation by -sign

$- f (x) = - (\frac{x^{2} - 1}{x + 4}) - f (x) = \frac{1 - x^{2}}{x + 4}$

Part (f) Step 1. We find the value of f(x+1)Putting x=x+1 in the given question.

$f (x + 1) = \frac{{(x + 1)}^{2} - 1}{(x + 1) + 4}$

Using the formula ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$

$f (x + 1) = \frac{x^{2} + 2 x + 1 - 1}{x + 1 + 4} f (x + 1) = \frac{x^{2} + 2 x}{x + 5} f (x + 1) = \frac{x (x + 2)}{x + 5}$

Part (g) Step 1. We find the value of f(x)

The value of $f (x) = \frac{x^{2} - 1}{x + 4}$

Part (h) Step 1. We find the value of f(x+h)Putting x=x+h in the given question.

$f (x + h) = \frac{{(x + h)}^{2} - 1}{(x + h) + 4}$

Using the formula

{(a + b)}^{2} = a^{2} + 2 a b + b^{2}

$f (x + h) = \frac{{x^{2} + 2 x h + h}^{2} - 1}{x + h + 4}$

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In Problems 39– 46, find the following for each function:
$(a) f (0) (b) f (1) (c) f (- 1) (d) f (- x) (e) - f (x) (f) f (x + 1) (g) f (x) (h) f (x + h)$
$f (x) = \frac{x^{2} - 1}{x + 4}$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. We find the value of f(0)Putting x=0 in the given question.

Part (b) Step 1. We find the value of f(1)Putting x=1 in the given question.

Part (c) Step 1. We find the value of f(-1)Putting x=-1 in the given question.

Part (d) Step 1. We find the value of f(-x)Putting x=-x in the given question.

Part (e) Step 1. We find the value of -f(x)To find the value we multiply the given equation by -sign

Part (f) Step 1. We find the value of f(x+1)Putting x=x+1 in the given question.

Part (g) Step 1. We find the value of f(x)

Part (h) Step 1. We find the value of f(x+h)Putting x=x+h in the given question.

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In Problems 39– 46, find the following for each function:(a)f(0)(b)f(1)(c)f(-1)(d)f(-x)(e)-f(x)(f)f(x+1)(g)f(x)(h)f(x+h)f(x)=x2-1x+4

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. We find the value of f(0)Putting x=0 in the given question.

Part (b) Step 1. We find the value of f(1)Putting x=1 in the given question.

Part (c) Step 1. We find the value of f(-1)Putting x=-1 in the given question.

Part (d) Step 1. We find the value of f(-x)Putting x=-x in the given question.

Part (e) Step 1. We find the value of -f(x)To find the value we multiply the given equation by -sign

Part (f) Step 1. We find the value of f(x+1)Putting x=x+1 in the given question.

Part (g) Step 1. We find the value of f(x)

Part (h) Step 1. We find the value of f(x+h)Putting x=x+h in the given question.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In Problems 39– 46, find the following for each function:
$(a) f (0) (b) f (1) (c) f (- 1) (d) f (- x) (e) - f (x) (f) f (x + 1) (g) f (x) (h) f (x + h)$
$f (x) = \frac{x^{2} - 1}{x + 4}$