QuestionFind $g(f(5 x))$ for $f(x)=2 x-1$ and $g(x)=3 x^{2}-7$ . Choose from: A, B, C, D.

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as $f(x)=x-1$ . The function $g(x)$ is defined as $g(x)=3x^{}-7$
3. We need to find the value of $g(f(5x))$

STEP 2

To find $g(f(5x))$ , we first need to find the value of $f(5x)$ .
$f(5x) =2(5x) -1$

STEP 3

implify the expression $f(5x)$ .
$f(5x) =10x -1$

STEP 4

Now that we have the value of $f(x)$ , we can substitute this into the function $g(x)$ to find $g(f(x))$ .
$g(f(x)) = g(10x -1)$

STEP 5

Substitute $10x -1$ into the function $g(x)$ .
$g(10x -1) =3(10x -1)^{2} -7$

STEP 6

Expand the square in the expression.
$g(10x -1) =3(100x^{2} -20x +1) -$

STEP 7

istribute the3 across the terms inside the parentheses.
$g(10x -1) =300x^{2} -60x +3 -7$

STEP 8

implify the expression to find the final form of $g(f(5x))$ .
$g(f(5x)) =300x^{2} -60x -4$ So, the answer is B. $300 x^{2}-60 x-4$ .

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QuestionFind $g(f(5 x))$ for $f(x)=2 x-1$ and $g(x)=3 x^{2}-7$ . Choose from: A, B, C, D.

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is defined as $f(x)=x-1$ . The function $g(x)$ is defined as $g(x)=3x^{}-7$
3. We need to find the value of $g(f(5x))$

STEP 2

To find $g(f(5x))$ , we first need to find the value of $f(5x)$ .
$f(5x) =2(5x) -1$

STEP 3

implify the expression $f(5x)$ .
$f(5x) =10x -1$

STEP 4

Now that we have the value of $f(x)$ , we can substitute this into the function $g(x)$ to find $g(f(x))$ .
$g(f(x)) = g(10x -1)$

STEP 5

Substitute $10x -1$ into the function $g(x)$ .
$g(10x -1) =3(10x -1)^{2} -7$

STEP 6

Expand the square in the expression.
$g(10x -1) =3(100x^{2} -20x +1) -$

STEP 7

istribute the3 across the terms inside the parentheses.
$g(10x -1) =300x^{2} -60x +3 -7$

STEP 8

implify the expression to find the final form of $g(f(5x))$ .
$g(f(5x)) =300x^{2} -60x -4$ So, the answer is B. $300 x^{2}-60 x-4$ .

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QuestionFind g(f(5x))g(f(5 x))g(f(5x)) for f(x)=2x−1f(x)=2 x-1f(x)=2x−1 and g(x)=3x2−7g(x)=3 x^{2}-7g(x)=3x2−7. Choose from: A, B, C, D.

Studdy Solution

STEP 1

Assumptions1. The function f(x)f(x)f(x) is defined as f(x)=x−1f(x)=x-1f(x)=x−1 . The function g(x)g(x)g(x) is defined as g(x)=3x−7g(x)=3x^{}-7g(x)=3x−73. We need to find the value of g(f(5x))g(f(5x))g(f(5x))

STEP 2

To find g(f(5x))g(f(5x))g(f(5x)), we first need to find the value of f(5x)f(5x)f(5x).f(5x)=2(5x)−1f(5x) =2(5x) -1f(5x)=2(5x)−1

STEP 3

implify the expression f(5x)f(5x)f(5x).f(5x)=10x−1f(5x) =10x -1f(5x)=10x−1

STEP 4

Now that we have the value of f(x)f(x)f(x), we can substitute this into the function g(x)g(x)g(x) to find g(f(x))g(f(x))g(f(x)).g(f(x))=g(10x−1)g(f(x)) = g(10x -1)g(f(x))=g(10x−1)

STEP 5

Substitute 10x−110x -110x−1 into the function g(x)g(x)g(x).g(10x−1)=3(10x−1)2−7g(10x -1) =3(10x -1)^{2} -7g(10x−1)=3(10x−1)2−7

STEP 6

Expand the square in the expression.g(10x−1)=3(100x2−20x+1)−g(10x -1) =3(100x^{2} -20x +1) -g(10x−1)=3(100x2−20x+1)−

STEP 7

istribute the3 across the terms inside the parentheses.g(10x−1)=300x2−60x+3−7g(10x -1) =300x^{2} -60x +3 -7g(10x−1)=300x2−60x+3−7

STEP 8

implify the expression to find the final form of g(f(5x))g(f(5x))g(f(5x)).g(f(5x))=300x2−60x−4g(f(5x)) =300x^{2} -60x -4g(f(5x))=300x2−60x−4So, the answer is B. 300x2−60x−4300 x^{2}-60 x-4300x2−60x−4.

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QuestionFind $g(f(5 x))$ for $f(x)=2 x-1$ and $g(x)=3 x^{2}-7$ . Choose from: A, B, C, D.

Assumptions1. The function $f(x)$ is defined as $f(x)=x-1$ . The function $g(x)$ is defined as $g(x)=3x^{}-7$
3. We need to find the value of $g(f(5x))$

To find $g(f(5x))$ , we first need to find the value of $f(5x)$ .
$f(5x) =2(5x) -1$

implify the expression $f(5x)$ .
$f(5x) =10x -1$

Now that we have the value of $f(x)$ , we can substitute this into the function $g(x)$ to find $g(f(x))$ .
$g(f(x)) = g(10x -1)$

Substitute $10x -1$ into the function $g(x)$ .
$g(10x -1) =3(10x -1)^{2} -7$

Expand the square in the expression.
$g(10x -1) =3(100x^{2} -20x +1) -$

istribute the3 across the terms inside the parentheses.
$g(10x -1) =300x^{2} -60x +3 -7$

implify the expression to find the final form of $g(f(5x))$ .
$g(f(5x)) =300x^{2} -60x -4$ So, the answer is B. $300 x^{2}-60 x-4$ .