QuestionEvaluate the function $f(x)=4 x^{2}+2 x-2$ at these points: (a) $f(0)$ , (b) $f(5)$ , (c) $f(-5)$ , (d) $f(-x)$ , (e) $-f(x)$ , (f) $f(x+1)$ , (g) $f(5 x)$ , (h) $f(x+h)$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=4 x^{}+ x-$ . We need to find the value of the function at various points and expressions

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

Calculate the value of $f(5)$ .
$f(5)=4(5)^{2}+2(5)-2 =108$

STEP 6

(c) To find $f(-5)$ , we substitute $x=-5$ into the function.
$f(-5)=4(-5)^{2}+2(-5)-2$

STEP 7

Calculate the value of $f(-5)$ .
$f(-5)=4(-5)^{2}+2(-5)-2 =88$

STEP 8

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

STEP 9

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

STEP 10

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

STEP 11

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

STEP 12

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

STEP 13

Expand and simplify the expression for $f(x+)$ .
$f(x+)=x^{2}+8x++2x+2-2 =x^{2}+10x+$

STEP 14

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

STEP 15

implify the expression for $f(5x)$ .
$f(5x)=100x^{2}+10x-2$

STEP 16

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

STEP 17

Expand and simplify the expression for $f(x+h)$ .
$f(x+h)=4x^{2}+xh+4h^{2}+2x+2h-2 =4x^{2}+xh+4h^{2}+2x+2h-2$ So, the solutions are(a) $f(0)=-2$ (b) $f(5)=108$ (c) $f(-5)=88$ (d) $f(-x)=4x^{2}-2x-2$ (e) $-f(x)=-4x^{2}-2x+2$ (f) $f(x+)=4x^{2}+10x+4$ (g) $f(5x)=100x^{2}+10x-2$ (h) $f(x+h)=4x^{2}+xh+4h^{2}+2x+2h-2$

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QuestionEvaluate the function $f(x)=4 x^{2}+2 x-2$ at these points: (a) $f(0)$ , (b) $f(5)$ , (c) $f(-5)$ , (d) $f(-x)$ , (e) $-f(x)$ , (f) $f(x+1)$ , (g) $f(5 x)$ , (h) $f(x+h)$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=4 x^{}+ x-$ . We need to find the value of the function at various points and expressions

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

Calculate the value of $f(5)$ .
$f(5)=4(5)^{2}+2(5)-2 =108$

STEP 6

(c) To find $f(-5)$ , we substitute $x=-5$ into the function.
$f(-5)=4(-5)^{2}+2(-5)-2$

STEP 7

Calculate the value of $f(-5)$ .
$f(-5)=4(-5)^{2}+2(-5)-2 =88$

STEP 8

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

STEP 9

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

STEP 10

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

STEP 11

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

STEP 12

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

STEP 13

Expand and simplify the expression for $f(x+)$ .
$f(x+)=x^{2}+8x++2x+2-2 =x^{2}+10x+$

STEP 14

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

STEP 15

implify the expression for $f(5x)$ .
$f(5x)=100x^{2}+10x-2$

STEP 16

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

STEP 17

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QuestionEvaluate the function f(x)=4x2+2x−2f(x)=4 x^{2}+2 x-2f(x)=4x2+2x−2 at these points: (a) f(0)f(0)f(0), (b) f(5)f(5)f(5), (c) f(−5)f(-5)f(−5), (d) f(−x)f(-x)f(−x), (e) −f(x)-f(x)−f(x), (f) f(x+1)f(x+1)f(x+1), (g) f(5x)f(5 x)f(5x), (h) f(x+h)f(x+h)f(x+h).

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=4x+x−f(x)=4 x^{}+ x-f(x)=4x+x− . We need to find the value of the function at various points and expressions

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+2(0)−2f(0)=4(0)^{2}+2(0)-2f(0)=4(0)2+2(0)−2

STEP 3

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

STEP 4

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

STEP 5

Calculate the value of f(5)f(5)f(5).f(5)=4(5)2+2(5)−2=108f(5)=4(5)^{2}+2(5)-2 =108f(5)=4(5)2+2(5)−2=108

STEP 6

(c) To find f(−5)f(-5)f(−5), we substitute x=−5x=-5x=−5 into the function.f(−5)=4(−5)2+2(−5)−2f(-5)=4(-5)^{2}+2(-5)-2f(−5)=4(−5)2+2(−5)−2

STEP 7

Calculate the value of f(−5)f(-5)f(−5).f(−5)=4(−5)2+2(−5)−2=88f(-5)=4(-5)^{2}+2(-5)-2 =88f(−5)=4(−5)2+2(−5)−2=88

STEP 8

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

STEP 9

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

STEP 10

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

STEP 11

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

STEP 12

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

STEP 13

Expand and simplify the expression for f(x+)f(x+)f(x+).f(x+)=x2+8x++2x+2−2=x2+10x+f(x+)=x^{2}+8x++2x+2-2 =x^{2}+10x+f(x+)=x2+8x++2x+2−2=x2+10x+

STEP 14

(g) To find f(x)f(x)f(x), we substitute xxx into the function.f(x)=4(x)2+2(x)−2f(x)=4(x)^{2}+2(x)-2f(x)=4(x)2+2(x)−2

STEP 15

implify the expression for f(5x)f(5x)f(5x).f(5x)=100x2+10x−2f(5x)=100x^{2}+10x-2f(5x)=100x2+10x−2

STEP 16

(h) To find f(x+h)f(x+h)f(x+h), we substitute x+hx+hx+h into the function.f(x+h)=4(x+h)2+2(x+h)−2f(x+h)=4(x+h)^{2}+2(x+h)-2f(x+h)=4(x+h)2+2(x+h)−2

STEP 17

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QuestionEvaluate the function $f(x)=4 x^{2}+2 x-2$ at these points: (a) $f(0)$ , (b) $f(5)$ , (c) $f(-5)$ , (d) $f(-x)$ , (e) $-f(x)$ , (f) $f(x+1)$ , (g) $f(5 x)$ , (h) $f(x+h)$ .

Assumptions1. The function is $f(x)=4 x^{}+ x-$ . We need to find the value of the function at various points and expressions

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

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

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

Calculate the value of $f(5)$ .
$f(5)=4(5)^{2}+2(5)-2 =108$

(c) To find $f(-5)$ , we substitute $x=-5$ into the function.
$f(-5)=4(-5)^{2}+2(-5)-2$

Calculate the value of $f(-5)$ .
$f(-5)=4(-5)^{2}+2(-5)-2 =88$

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

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

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

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

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

Expand and simplify the expression for $f(x+)$ .
$f(x+)=x^{2}+8x++2x+2-2 =x^{2}+10x+$

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

implify the expression for $f(5x)$ .
$f(5x)=100x^{2}+10x-2$

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