QuestionEvaluate the function $f(x)=4x^2+3x-2$ at these points: (a) $f(0)$ , (b) $f(2)$ , (c) $f(-2)$ , (d) $f(-x)$ , (e) $-f(x)$ , (f) $f(x+3)$ , (h) $f(x+h)$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=4x^+3x-$ . We need to find the value of the function for different inputs

STEP 2

(a) To find $f(0)$ , we substitute $x=0$ into the function.
$f(0)=4(0)^2+(0)-2$

STEP 3

Calculate the value of $f(0)$ .
$f(0)=(0)^2+3(0)-2 = -2$

STEP 4

(b) To find $f(2)$ , we substitute $x=2$ into the function.
$f(2)=4(2)^2+3(2)-2$

STEP 5

Calculate the value of $f(2)$ .
$f(2)=4(2)^2+3(2)-2 =20$

STEP 6

(c) To find $f(-2)$ , we substitute $x=-2$ into the function.
$f(-2)=4(-2)^2+3(-2)-2$

STEP 7

Calculate the value of $f(-2)$ .
$f(-2)=4(-2)^2+3(-2)-2 =$

STEP 8

(d) To find $f(-x)$ , we substitute $-x$ for $x$ in the function.
$f(-x)=4(-x)^2+3(-x)-2$

STEP 9

implify the expression for $f(-x)$ .
$f(-x)=4x^2-3x-2$

STEP 10

(e) To find $-f(x)$ , we multiply the function by $-$ .
$-f(x)=-(4x^2+3x-2)$

STEP 11

implify the expression for $-f(x)$ .
$-f(x)=-4x^-3x+$

STEP 12

(f) To find $f(x+)$ , we substitute $x+$ for $x$ in the function.
$f(x+)=4(x+)^2+(x+)-2$

STEP 13

Expand and simplify the expression for $f(x+3)$ .
$f(x+3)=(x^2+6x+9)+3x+9-2=x^2+27x+32$

STEP 14

(h) To find $f(x+h)$ , we substitute $x+h$ for $x$ in the function.
$f(x+h)=4(x+h)^2+3(x+h)-2$

STEP 15

Expand and simplify the expression for $f(x+h)$ .
$f(x+h)=4(x^2+2hx+h^2)+3x+3h-2=4x^2+8hx+4h^2+3x+3h-2$ So, the solutions are(a) $f(0)=-2$ (b) $f(2)=20$ (c) $f(-2)=8$ (d) $f(-x)=4x^2-3x-2$ (e) $-f(x)=-4x^2-3x+2$ (f) $f(x+3)=4x^2+27x+32$ (h) $f(x+h)=4x^2+8hx+4h^2+3x+3h-2$

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QuestionEvaluate the function $f(x)=4x^2+3x-2$ at these points: (a) $f(0)$ , (b) $f(2)$ , (c) $f(-2)$ , (d) $f(-x)$ , (e) $-f(x)$ , (f) $f(x+3)$ , (h) $f(x+h)$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=4x^+3x-$ . We need to find the value of the function for different inputs

STEP 2

(a) To find $f(0)$ , we substitute $x=0$ into the function.
$f(0)=4(0)^2+(0)-2$

STEP 3

Calculate the value of $f(0)$ .
$f(0)=(0)^2+3(0)-2 = -2$

STEP 4

(b) To find $f(2)$ , we substitute $x=2$ into the function.
$f(2)=4(2)^2+3(2)-2$

STEP 5

Calculate the value of $f(2)$ .
$f(2)=4(2)^2+3(2)-2 =20$

STEP 6

(c) To find $f(-2)$ , we substitute $x=-2$ into the function.
$f(-2)=4(-2)^2+3(-2)-2$

STEP 7

Calculate the value of $f(-2)$ .
$f(-2)=4(-2)^2+3(-2)-2 =$

STEP 8

(d) To find $f(-x)$ , we substitute $-x$ for $x$ in the function.
$f(-x)=4(-x)^2+3(-x)-2$

STEP 9

implify the expression for $f(-x)$ .
$f(-x)=4x^2-3x-2$

STEP 10

(e) To find $-f(x)$ , we multiply the function by $-$ .
$-f(x)=-(4x^2+3x-2)$

STEP 11

implify the expression for $-f(x)$ .
$-f(x)=-4x^-3x+$

STEP 12

(f) To find $f(x+)$ , we substitute $x+$ for $x$ in the function.
$f(x+)=4(x+)^2+(x+)-2$

STEP 13

Expand and simplify the expression for $f(x+3)$ .
$f(x+3)=(x^2+6x+9)+3x+9-2=x^2+27x+32$

STEP 14

(h) To find $f(x+h)$ , we substitute $x+h$ for $x$ in the function.
$f(x+h)=4(x+h)^2+3(x+h)-2$

STEP 15

Expand and simplify the expression for $f(x+h)$ .
$f(x+h)=4(x^2+2hx+h^2)+3x+3h-2=4x^2+8hx+4h^2+3x+3h-2$ So, the solutions are(a) $f(0)=-2$ (b) $f(2)=20$ (c) $f(-2)=8$ (d) $f(-x)=4x^2-3x-2$ (e) $-f(x)=-4x^2-3x+2$ (f) $f(x+3)=4x^2+27x+32$ (h) $f(x+h)=4x^2+8hx+4h^2+3x+3h-2$

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QuestionEvaluate the function f(x)=4x2+3x−2f(x)=4x^2+3x-2f(x)=4x2+3x−2 at these points: (a) f(0)f(0)f(0), (b) f(2)f(2)f(2), (c) f(−2)f(-2)f(−2), (d) f(−x)f(-x)f(−x), (e) −f(x)-f(x)−f(x), (f) f(x+3)f(x+3)f(x+3), (h) f(x+h)f(x+h)f(x+h).

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=4x+3x−f(x)=4x^+3x-f(x)=4x+3x− . We need to find the value of the function for different inputs

STEP 2

(a) To find f(0)f(0)f(0), we substitute x=0x=0x=0 into the function.f(0)=4(0)2+(0)−2f(0)=4(0)^2+(0)-2f(0)=4(0)2+(0)−2

STEP 3

Calculate the value of f(0)f(0)f(0).f(0)=(0)2+3(0)−2=−2f(0)=(0)^2+3(0)-2 = -2f(0)=(0)2+3(0)−2=−2

STEP 4

(b) To find f(2)f(2)f(2), we substitute x=2x=2x=2 into the function.f(2)=4(2)2+3(2)−2f(2)=4(2)^2+3(2)-2f(2)=4(2)2+3(2)−2

STEP 5

Calculate the value of f(2)f(2)f(2).f(2)=4(2)2+3(2)−2=20f(2)=4(2)^2+3(2)-2 =20f(2)=4(2)2+3(2)−2=20

STEP 6

(c) To find f(−2)f(-2)f(−2), we substitute x=−2x=-2x=−2 into the function.f(−2)=4(−2)2+3(−2)−2f(-2)=4(-2)^2+3(-2)-2f(−2)=4(−2)2+3(−2)−2

STEP 7

Calculate the value of f(−2)f(-2)f(−2).f(−2)=4(−2)2+3(−2)−2=f(-2)=4(-2)^2+3(-2)-2 =f(−2)=4(−2)2+3(−2)−2=

STEP 8

(d) To find f(−x)f(-x)f(−x), we substitute −x-x−x for xxx in the function.f(−x)=4(−x)2+3(−x)−2f(-x)=4(-x)^2+3(-x)-2f(−x)=4(−x)2+3(−x)−2

STEP 9

implify the expression for f(−x)f(-x)f(−x).f(−x)=4x2−3x−2f(-x)=4x^2-3x-2f(−x)=4x2−3x−2

STEP 10

(e) To find −f(x)-f(x)−f(x), we multiply the function by −-−.−f(x)=−(4x2+3x−2)-f(x)=-(4x^2+3x-2)−f(x)=−(4x2+3x−2)

STEP 11

implify the expression for −f(x)-f(x)−f(x).−f(x)=−4x−3x+-f(x)=-4x^-3x+−f(x)=−4x−3x+

STEP 12

(f) To find f(x+)f(x+)f(x+), we substitute x+x+x+ for xxx in the function.f(x+)=4(x+)2+(x+)−2f(x+)=4(x+)^2+(x+)-2f(x+)=4(x+)2+(x+)−2

STEP 13

Expand and simplify the expression for f(x+3)f(x+3)f(x+3).f(x+3)=(x2+6x+9)+3x+9−2=x2+27x+32f(x+3)=(x^2+6x+9)+3x+9-2=x^2+27x+32f(x+3)=(x2+6x+9)+3x+9−2=x2+27x+32

STEP 14

(h) To find f(x+h)f(x+h)f(x+h), we substitute x+hx+hx+h for xxx in the function.f(x+h)=4(x+h)2+3(x+h)−2f(x+h)=4(x+h)^2+3(x+h)-2f(x+h)=4(x+h)2+3(x+h)−2

STEP 15

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QuestionEvaluate the function $f(x)=4x^2+3x-2$ at these points: (a) $f(0)$ , (b) $f(2)$ , (c) $f(-2)$ , (d) $f(-x)$ , (e) $-f(x)$ , (f) $f(x+3)$ , (h) $f(x+h)$ .

Assumptions1. The function is $f(x)=4x^+3x-$ . We need to find the value of the function for different inputs

(a) To find $f(0)$ , we substitute $x=0$ into the function.
$f(0)=4(0)^2+(0)-2$

Calculate the value of $f(0)$ .
$f(0)=(0)^2+3(0)-2 = -2$

(b) To find $f(2)$ , we substitute $x=2$ into the function.
$f(2)=4(2)^2+3(2)-2$

Calculate the value of $f(2)$ .
$f(2)=4(2)^2+3(2)-2 =20$

(c) To find $f(-2)$ , we substitute $x=-2$ into the function.
$f(-2)=4(-2)^2+3(-2)-2$

Calculate the value of $f(-2)$ .
$f(-2)=4(-2)^2+3(-2)-2 =$

(d) To find $f(-x)$ , we substitute $-x$ for $x$ in the function.
$f(-x)=4(-x)^2+3(-x)-2$

implify the expression for $f(-x)$ .
$f(-x)=4x^2-3x-2$

(e) To find $-f(x)$ , we multiply the function by $-$ .
$-f(x)=-(4x^2+3x-2)$

implify the expression for $-f(x)$ .
$-f(x)=-4x^-3x+$

(f) To find $f(x+)$ , we substitute $x+$ for $x$ in the function.
$f(x+)=4(x+)^2+(x+)-2$

Expand and simplify the expression for $f(x+3)$ .
$f(x+3)=(x^2+6x+9)+3x+9-2=x^2+27x+32$

(h) To find $f(x+h)$ , we substitute $x+h$ for $x$ in the function.
$f(x+h)=4(x+h)^2+3(x+h)-2$