QuestionOperate the functions: $f(x)=x-1$ , $g(x)=x^{2}-1$ , $h(x)=3x^{2}-2x-1$ . Find $(g+h)(x)$ , $(h-f)(x)$ , $(f-h)(x)$ .

Studdy Solution

STEP 1

Assumptions1. The functions are defined as follows - $f(x) = x -1$ - $g(x) = x^{} -1$ - $h(x) =3x^{} -x -1$
. The operations to be performed are addition and subtraction of functions.

STEP 2

To find $(g+h)(x)$ , we need to add the functions $g(x)$ and $h(x)$ .
$(g+h)(x) = g(x) + h(x)$

STEP 3

Substitute the given functions into the equation.
$(g+h)(x) = (x^{2} -1) + (3x^{2} -2x -1)$

STEP 4

Combine like terms.
$(g+h)(x) =4x^{2} -2x -2$

STEP 5

To find $(h-f)(x)$ , we need to subtract the function $f(x)$ from $h(x)$ .
$(h-f)(x) = h(x) - f(x)$

STEP 6

Substitute the given functions into the equation.
$(h-f)(x) = (3x^{2} -2x -1) - (x -1)$

STEP 7

istribute the negative sign and combine like terms.
$(h-f)(x) =3x^{2} -3x$

STEP 8

To find $(f-h)(x)$ , we need to subtract the function $h(x)$ from $f(x)$ .
$(f-h)(x) = f(x) - h(x)$

STEP 9

Substitute the given functions into the equation.
$(f-h)(x) = (x -) - (3x^{2} -2x -)$

STEP 10

istribute the negative sign and combine like terms.
$(f-h)(x) = -3x^{2} +3x$ So, the results are. $(g+h)(x) =4x^{2} -2x -2$
2. $(h-f)(x) =3x^{2} -3x$
3. $(f-h)(x) = -3x^{2} +3x$

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QuestionOperate the functions: $f(x)=x-1$ , $g(x)=x^{2}-1$ , $h(x)=3x^{2}-2x-1$ . Find $(g+h)(x)$ , $(h-f)(x)$ , $(f-h)(x)$ .

Studdy Solution

STEP 1

Assumptions1. The functions are defined as follows - $f(x) = x -1$ - $g(x) = x^{} -1$ - $h(x) =3x^{} -x -1$
. The operations to be performed are addition and subtraction of functions.

STEP 2

To find $(g+h)(x)$ , we need to add the functions $g(x)$ and $h(x)$ .
$(g+h)(x) = g(x) + h(x)$

STEP 3

Substitute the given functions into the equation.
$(g+h)(x) = (x^{2} -1) + (3x^{2} -2x -1)$

STEP 4

Combine like terms.
$(g+h)(x) =4x^{2} -2x -2$

STEP 5

To find $(h-f)(x)$ , we need to subtract the function $f(x)$ from $h(x)$ .
$(h-f)(x) = h(x) - f(x)$

STEP 6

Substitute the given functions into the equation.
$(h-f)(x) = (3x^{2} -2x -1) - (x -1)$

STEP 7

istribute the negative sign and combine like terms.
$(h-f)(x) =3x^{2} -3x$

STEP 8

To find $(f-h)(x)$ , we need to subtract the function $h(x)$ from $f(x)$ .
$(f-h)(x) = f(x) - h(x)$

STEP 9

Substitute the given functions into the equation.
$(f-h)(x) = (x -) - (3x^{2} -2x -)$

STEP 10

istribute the negative sign and combine like terms.
$(f-h)(x) = -3x^{2} +3x$ So, the results are. $(g+h)(x) =4x^{2} -2x -2$
2. $(h-f)(x) =3x^{2} -3x$
3. $(f-h)(x) = -3x^{2} +3x$

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QuestionOperate the functions: f(x)=x−1f(x)=x-1f(x)=x−1, g(x)=x2−1g(x)=x^{2}-1g(x)=x2−1, h(x)=3x2−2x−1h(x)=3x^{2}-2x-1h(x)=3x2−2x−1. Find (g+h)(x)(g+h)(x)(g+h)(x), (h−f)(x)(h-f)(x)(h−f)(x), (f−h)(x)(f-h)(x)(f−h)(x).

Studdy Solution

STEP 1

Assumptions1. The functions are defined as follows - f(x)=x−1f(x) = x -1f(x)=x−1 - g(x)=x−1g(x) = x^{} -1g(x)=x−1 - h(x)=3x−x−1h(x) =3x^{} -x -1h(x)=3x−x−1. The operations to be performed are addition and subtraction of functions.

STEP 2

To find (g+h)(x)(g+h)(x)(g+h)(x), we need to add the functions g(x)g(x)g(x) and h(x)h(x)h(x).(g+h)(x)=g(x)+h(x)(g+h)(x) = g(x) + h(x)(g+h)(x)=g(x)+h(x)

STEP 3

Substitute the given functions into the equation.(g+h)(x)=(x2−1)+(3x2−2x−1)(g+h)(x) = (x^{2} -1) + (3x^{2} -2x -1)(g+h)(x)=(x2−1)+(3x2−2x−1)

STEP 4

Combine like terms.(g+h)(x)=4x2−2x−2(g+h)(x) =4x^{2} -2x -2(g+h)(x)=4x2−2x−2

STEP 5

To find (h−f)(x)(h-f)(x)(h−f)(x), we need to subtract the function f(x)f(x)f(x) from h(x)h(x)h(x).(h−f)(x)=h(x)−f(x)(h-f)(x) = h(x) - f(x)(h−f)(x)=h(x)−f(x)

STEP 6

Substitute the given functions into the equation.(h−f)(x)=(3x2−2x−1)−(x−1)(h-f)(x) = (3x^{2} -2x -1) - (x -1)(h−f)(x)=(3x2−2x−1)−(x−1)

STEP 7

istribute the negative sign and combine like terms.(h−f)(x)=3x2−3x(h-f)(x) =3x^{2} -3x(h−f)(x)=3x2−3x

STEP 8

To find (f−h)(x)(f-h)(x)(f−h)(x), we need to subtract the function h(x)h(x)h(x) from f(x)f(x)f(x).(f−h)(x)=f(x)−h(x)(f-h)(x) = f(x) - h(x)(f−h)(x)=f(x)−h(x)

STEP 9

Substitute the given functions into the equation.(f−h)(x)=(x−)−(3x2−2x−)(f-h)(x) = (x -) - (3x^{2} -2x -)(f−h)(x)=(x−)−(3x2−2x−)

STEP 10

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QuestionOperate the functions: $f(x)=x-1$ , $g(x)=x^{2}-1$ , $h(x)=3x^{2}-2x-1$ . Find $(g+h)(x)$ , $(h-f)(x)$ , $(f-h)(x)$ .

Assumptions1. The functions are defined as follows - $f(x) = x -1$ - $g(x) = x^{} -1$ - $h(x) =3x^{} -x -1$
. The operations to be performed are addition and subtraction of functions.

To find $(g+h)(x)$ , we need to add the functions $g(x)$ and $h(x)$ .
$(g+h)(x) = g(x) + h(x)$

Substitute the given functions into the equation.
$(g+h)(x) = (x^{2} -1) + (3x^{2} -2x -1)$

Combine like terms.
$(g+h)(x) =4x^{2} -2x -2$

To find $(h-f)(x)$ , we need to subtract the function $f(x)$ from $h(x)$ .
$(h-f)(x) = h(x) - f(x)$

Substitute the given functions into the equation.
$(h-f)(x) = (3x^{2} -2x -1) - (x -1)$

istribute the negative sign and combine like terms.
$(h-f)(x) =3x^{2} -3x$

To find $(f-h)(x)$ , we need to subtract the function $h(x)$ from $f(x)$ .
$(f-h)(x) = f(x) - h(x)$

Substitute the given functions into the equation.
$(f-h)(x) = (x -) - (3x^{2} -2x -)$