Chapter 15: Chapter 15

Problem 1

For each function, evaluate (a) $f(0,0)$; (b) $f(1,0) ;$ (c) $f(0,-1)$; (d) $f(a, 2) ;$ (e) $f(y, x)$;(f) $f(x+h, y+k)$ HINT [See Quick Examples page 1080.] $$ f(x, y)=x^{2}+y^{2}-x+1 $$

Short Answer

Expert verified

The short answers for the given function, $f(x,y) = x^2 + y^2 - x + 1$, evaluated at different inputs are: (a) $f(0,0) = 1$ (b) $f(1,0) = 1$ (c) $f(0,-1) = 2$ (d) $f(a,2) = a^2 - a + 5$ (e) $f(y,x) = y^2 + x^2 - y + 1$ (f) $f(x+h, y+k) = x^2 + 2xh + h^2 + y^2 + 2yk + k^2 - x - h + 1$

See the step by step solution

Step by step solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: (a)

: To find $f(0,0)$, we plug in $x = 0$ and $y = 0$ into the function: $$ f(0, 0) = (0)^2 + (0)^2 - (0) + 1 = 0 + 0 + 1 = 1 $$

Step 2: (b)

: To find $f(1,0)$, we plug in $x = 1$ and $y = 0$ into the function: $$ f(1, 0) = (1)^2 + (0)^2 - (1) + 1 = 1 + 0 - 1 + 1 = 1 $$

Step 3: (c)

: To find $f(0,-1)$, we plug in $x = 0$ and $y = -1$ into the function: $$ f(0, -1) = (0)^2 + (-1)^2 - (0) + 1 = 0 + 1 + 1 = 2 $$

Step 4: (d)

: To find $f(a, 2)$, we plug in $x = a$ and $y = 2$ into the function: $$ f(a, 2) = a^2 + (2)^2 - a + 1 = a^2 + 4 - a + 1 = a^2 - a + 5 $$

Step 5: (e)

: To find $f(y, x)$, we plug in $x = y$ and $y = x$ into the function: $$ f(y, x) = y^2 + x^2 - y + 1 $$

Step 6: (f)

: To find $f(x+h, y+k)$, we plug in $x = x + h$ and $y = y + k$ into the function: $$ f(x+h, y+k) = (x + h)^2 + (y + k)^2 - (x + h) + 1 = x^2 + 2xh + h^2 + y^2 + 2yk + k^2 - x - h + 1 $$

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Recommended explanations on Math Textbooks

Select your language

Chapter 15: Chapter 15

For each function, evaluate (a) \(f(0,0)\); (b) \(f(1,0) ;\) (c) \(f(0,-1)\); (d) \(f(a, 2) ;\) (e) \(f(y, x)\);(f) \(f(x+h, y+k)\) HINT [See Quick Examples page 1080.] $$ f(x, y)=x^{2}+y^{2}-x+1 $$

Short Answer

Step by step solution

Unlock all solutions

Step 1: (a)

Step 2: (b)

Step 3: (c)

Step 4: (d)

Step 5: (e)

Step 6: (f)

Access millions of textbook solutions in one place

Most popular questions from this chapter

More chapters from the book ‘Finite Mathematics and Applied Calculus’

Chapter 0

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 16

Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Probability and Statistics

Decision Maths

Calculus

Statistics